Results of Confluent Hypergeometric Functions

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DLMF Formula Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
13.2.E1 z*diff(w, [z$(2)])+(b - z)* diff(w, z)- a*w = 0 z*D[w, {z, 2}]+(b - z)* D[w, z]- a*w = 0 Failure Failure
Fail
-0.-3.999999998*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}
-3.999999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}
-0.+3.999999998*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}
3.999999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[0.0, -4.0] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
-4.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 4.0] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
4.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
13.2.E2 KummerM(a, b, z)= sum((pochhammer(a, s))/(pochhammer(b, s)*factorial(s))*(z)^(s), s = 0..infinity) Hypergeometric1F1[a, b, z]= Sum[Divide[Pochhammer[a, s],Pochhammer[b, s]*(s)!]*(z)^(s), {s, 0, Infinity}] Successful Successful - -
13.2.E3 KummerM(a, b, z)/GAMMA(b)= sum((pochhammer(a, s))/(GAMMA(b + s)*factorial(s))*(z)^(s), s = 0..infinity) Hypergeometric1F1Regularized[a, b, z]= Sum[Divide[Pochhammer[a, s],Gamma[b + s]*(s)!]*(z)^(s), {s, 0, Infinity}] Successful Successful - -
13.2.E4 KummerM(a, b, z)= GAMMA(b)*KummerM(a, b, z)/GAMMA(b) Hypergeometric1F1[a, b, z]= Gamma[b]*Hypergeometric1F1Regularized[a, b, z] Successful Successful - -
13.2.E5 limit((KummerM(a, b, z))/(GAMMA(b)), b = - n)= KummerM(a, - n, z)/GAMMA(- n) Limit[Divide[Hypergeometric1F1[a, b, z],Gamma[b]], b -> - n]= Hypergeometric1F1Regularized[a, - n, z] Successful Successful - -
13.2.E5 KummerM(a, - n, z)/GAMMA(- n)=(pochhammer(a, n + 1))/(factorial(n + 1))*(z)^(n + 1)* KummerM(a + n + 1, n + 2, z) Hypergeometric1F1Regularized[a, - n, z]=Divide[Pochhammer[a, n + 1],(n + 1)!]*(z)^(n + 1)* Hypergeometric1F1[a + n + 1, n + 2, z] Failure Failure
Fail
Float(undefined)+Float(undefined)*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
Float(undefined)+Float(undefined)*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
Float(undefined)+Float(undefined)*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
Float(undefined)+Float(undefined)*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
Successful
13.2.E7 KummerU(- m, b, z)=(- 1)^(m)* pochhammer(b, m)*KummerM(- m, b, z) HypergeometricU[- m, b, z]=(- 1)^(m)* Pochhammer[b, m]*Hypergeometric1F1[- m, b, z] Failure Failure Skip Successful
13.2.E7 (- 1)^(m)* pochhammer(b, m)*KummerM(- m, b, z)=(- 1)^(m)* sum(binomial(m,s)*pochhammer(b + s, m - s)*(- z)^(s), s = 0..m) (- 1)^(m)* Pochhammer[b, m]*Hypergeometric1F1[- m, b, z]=(- 1)^(m)* Sum[Binomial[m,s]*Pochhammer[b + s, m - s]*(- z)^(s), {s, 0, m}] Successful Successful - -
13.2.E8 KummerU(a, a + n + 1, z)=((- 1)^(n)* pochhammer(1 - a - n, n))/((z)^(a + n))*KummerM(- n, 1 - a - n, z) HypergeometricU[a, a + n + 1, z]=Divide[(- 1)^(n)* Pochhammer[1 - a - n, n],(z)^(a + n)]*Hypergeometric1F1[- n, 1 - a - n, z] Failure Failure Skip Successful
13.2.E8 ((- 1)^(n)* pochhammer(1 - a - n, n))/((z)^(a + n))*KummerM(- n, 1 - a - n, z)= (z)^(- a)* sum(binomial(n,s)*pochhammer(a, s)*(z)^(- s), s = 0..n) Divide[(- 1)^(n)* Pochhammer[1 - a - n, n],(z)^(a + n)]*Hypergeometric1F1[- n, 1 - a - n, z]= (z)^(- a)* Sum[Binomial[n,s]*Pochhammer[a, s]*(z)^(- s), {s, 0, n}] Failure Failure Skip Successful
13.2.E9 KummerU(a, n + 1, z)=((- 1)^(n + 1))/(factorial(n)*GAMMA(a - n))*sum((pochhammer(a, k))/(pochhammer(n + 1, k)*factorial(k))*(z)^(k)*(ln(z)+ Psi(a + k)- Psi(1 + k)- Psi(n + k + 1)), k = 0..infinity)+(1)/(GAMMA(a))*sum((factorial(k - 1)*pochhammer(1 - a + k, n - k))/(factorial(n - k))*(z)^(- k), k = 1..n) HypergeometricU[a, n + 1, z]=Divide[(- 1)^(n + 1),(n)!*Gamma[a - n]]*Sum[Divide[Pochhammer[a, k],Pochhammer[n + 1, k]*(k)!]*(z)^(k)*(Log[z]+ PolyGamma[a + k]- PolyGamma[1 + k]- PolyGamma[n + k + 1]), {k, 0, Infinity}]+Divide[1,Gamma[a]]*Sum[Divide[(k - 1)!*Pochhammer[1 - a + k, n - k],(n - k)!]*(z)^(- k), {k, 1, n}] Error Failure - Error
13.2.E10 KummerU(- m, n + 1, z)=(- 1)^(m)* pochhammer(n + 1, m)*KummerM(- m, n + 1, z) HypergeometricU[- m, n + 1, z]=(- 1)^(m)* Pochhammer[n + 1, m]*Hypergeometric1F1[- m, n + 1, z] Failure Failure Successful Successful
13.2.E10 (- 1)^(m)* pochhammer(n + 1, m)*KummerM(- m, n + 1, z)=(- 1)^(m)* sum(binomial(m,s)*pochhammer(n + s + 1, m - s)*(- z)^(s), s = 0..m) (- 1)^(m)* Pochhammer[n + 1, m]*Hypergeometric1F1[- m, n + 1, z]=(- 1)^(m)* Sum[Binomial[m,s]*Pochhammer[n + s + 1, m - s]*(- z)^(s), {s, 0, m}] Successful Successful - -
13.2.E11 KummerU(a, - n, z)= (z)^(n + 1)* KummerU(a + n + 1, n + 2, z) HypergeometricU[a, - n, z]= (z)^(n + 1)* HypergeometricU[a + n + 1, n + 2, z] Successful Successful - -
13.2.E12 KummerU(a, b, z*exp(2*Pi*I*m))=(2*Pi*I*exp(- Pi*I*b*m)*sin(Pi*b*m))/(GAMMA(1 + a - b)*sin(Pi*b))*KummerM(a, b, z)/GAMMA(b)+ exp(- 2*Pi*I*b*m)*KummerU(a, b, z) HypergeometricU[a, b, z*Exp[2*Pi*I*m]]=Divide[2*Pi*I*Exp[- Pi*I*b*m]*Sin[Pi*b*m],Gamma[1 + a - b]*Sin[Pi*b]]*Hypergeometric1F1Regularized[a, b, z]+ Exp[- 2*Pi*I*b*m]*HypergeometricU[a, b, z] Failure Failure
Fail
584.8702437+1098.665595*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}
448650.07-8984458.84*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}
-.361175805e11+.540703722e11*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}
1655.171849-5530.515123*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}
... skip entries to safe data
Skip
13.2.E33 (KummerM(a, b, z)/GAMMA(b))*diff((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)-diff(KummerM(a, b, z)/GAMMA(b), z)*((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))= sin(Pi*b)*(z)^(- b)* exp(z)/ Pi Wronskian[{Hypergeometric1F1Regularized[a, b, z], (z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z]}, z]= Sin[Pi*b]*(z)^(- b)* Exp[z]/ Pi Failure Failure Successful Skip
13.2.E34 (KummerM(a, b, z)/GAMMA(b))*diff(KummerU(a, b, z), z)-diff(KummerM(a, b, z)/GAMMA(b), z)*(KummerU(a, b, z))= -((z)^(- b)* exp(z))/(GAMMA(a)) Wronskian[{Hypergeometric1F1Regularized[a, b, z], HypergeometricU[a, b, z]}, z]= -Divide[(z)^(- b)* Exp[z],Gamma[a]] Failure Failure Successful Skip
13.2.E35 (KummerM(a, b, z)/GAMMA(b))*diff(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z), z)-diff(KummerM(a, b, z)/GAMMA(b), z)*(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z))=(exp(- b*Pi*I)*(z)^(- b)* exp(z))/(GAMMA(b - a)) Wronskian[{Hypergeometric1F1Regularized[a, b, z], Exp[z]*HypergeometricU[b - a, b, Exp[+ Pi*I]*z]}, z]=Divide[Exp[- b*Pi*I]*(z)^(- b)* Exp[z],Gamma[b - a]] Failure Failure Skip Skip
13.2.E35 (KummerM(a, b, z)/GAMMA(b))*diff(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z), z)-diff(KummerM(a, b, z)/GAMMA(b), z)*(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z))=(exp(+ b*Pi*I)*(z)^(- b)* exp(z))/(GAMMA(b - a)) Wronskian[{Hypergeometric1F1Regularized[a, b, z], Exp[z]*HypergeometricU[b - a, b, Exp[- Pi*I]*z]}, z]=Divide[Exp[+ b*Pi*I]*(z)^(- b)* Exp[z],Gamma[b - a]] Failure Failure Skip Skip
13.2.E36 ((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))*diff(KummerU(a, b, z), z)-diff((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)*(KummerU(a, b, z))= -((z)^(- b)* exp(z))/(GAMMA(a - b + 1)) Wronskian[{(z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z], HypergeometricU[a, b, z]}, z]= -Divide[(z)^(- b)* Exp[z],Gamma[a - b + 1]] Failure Failure Skip Skip
13.2.E37 ((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))*diff(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z), z)-diff((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)*(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z))= -((z)^(- b)* exp(z))/(GAMMA(1 - a)) Wronskian[{(z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z], Exp[z]*HypergeometricU[b - a, b, Exp[+ Pi*I]*z]}, z]= -Divide[(z)^(- b)* Exp[z],Gamma[1 - a]] Failure Failure Skip Successful
13.2.E37 ((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))*diff(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z), z)-diff((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)*(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z))= -((z)^(- b)* exp(z))/(GAMMA(1 - a)) Wronskian[{(z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z], Exp[z]*HypergeometricU[b - a, b, Exp[- Pi*I]*z]}, z]= -Divide[(z)^(- b)* Exp[z],Gamma[1 - a]] Failure Failure Skip Skip
13.2.E38 (KummerU(a, b, z))*diff(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z), z)-diff(KummerU(a, b, z), z)*(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z))= exp(+(a - b)* Pi*I)*(z)^(- b)* exp(z) Wronskian[{HypergeometricU[a, b, z], Exp[z]*HypergeometricU[b - a, b, Exp[+ Pi*I]*z]}, z]= Exp[+(a - b)* Pi*I]*(z)^(- b)* Exp[z] Failure Failure Skip
Fail
Complex[1040.14465936905, 3523.550863963589] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[13.933478379950422, -18.985981055998398] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[16167.755810004226, 20483.57845334895] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-167.2507901552425, 2.9337620233109254] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
13.2.E38 (KummerU(a, b, z))*diff(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z), z)-diff(KummerU(a, b, z), z)*(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z))= exp(-(a - b)* Pi*I)*(z)^(- b)* exp(z) Wronskian[{HypergeometricU[a, b, z], Exp[z]*HypergeometricU[b - a, b, Exp[- Pi*I]*z]}, z]= Exp[-(a - b)* Pi*I]*(z)^(- b)* Exp[z] Failure Failure Skip
Fail
Complex[-26409.287510504182, -21215.250458979182] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[17917.63845480152, -4449.098851771366] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[128856.58558615872, -203204.6357206061] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-130654.53246573739, 11199.95676626326] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
13.2.E39 KummerM(a, b, z)= exp(z)*KummerM(b - a, b, - z) Hypergeometric1F1[a, b, z]= Exp[z]*Hypergeometric1F1[b - a, b, - z] Failure Successful Successful -
13.2.E40 KummerU(a, b, z)= (z)^(1 - b)* KummerU(a - b + 1, 2 - b, z) HypergeometricU[a, b, z]= (z)^(1 - b)* HypergeometricU[a - b + 1, 2 - b, z] Successful Successful - -
13.2.E41 (1)/(GAMMA(b))*KummerM(a, b, z)=(exp(- a*Pi*I))/(GAMMA(b - a))*KummerU(a, b, z)+(exp(+(b - a)* Pi*I))/(GAMMA(a))*exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z) Divide[1,Gamma[b]]*Hypergeometric1F1[a, b, z]=Divide[Exp[- a*Pi*I],Gamma[b - a]]*HypergeometricU[a, b, z]+Divide[Exp[+(b - a)* Pi*I],Gamma[a]]*Exp[z]*HypergeometricU[b - a, b, Exp[+ Pi*I]*z] Failure Failure
Fail
17637856.16+44349536.15*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
78404.04567+70170.88583*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
23503366.51-739194412.4*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-413147.5251+1810381.777*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Skip
13.2.E41 (1)/(GAMMA(b))*KummerM(a, b, z)=(exp(+ a*Pi*I))/(GAMMA(b - a))*KummerU(a, b, z)+(exp(-(b - a)* Pi*I))/(GAMMA(a))*exp(z)*KummerU(b - a, b, exp(- Pi*I)*z) Divide[1,Gamma[b]]*Hypergeometric1F1[a, b, z]=Divide[Exp[+ a*Pi*I],Gamma[b - a]]*HypergeometricU[a, b, z]+Divide[Exp[-(b - a)* Pi*I],Gamma[a]]*Exp[z]*HypergeometricU[b - a, b, Exp[- Pi*I]*z] Failure Failure
Fail
8.816149469+15.35727015*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
3.036467728-4.734652938*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
237.2244957-69.52948040*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
40.35920508+88.71475163*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
... skip entries to safe data
Skip
13.2.E42 KummerU(a, b, z)=(GAMMA(1 - b))/(GAMMA(a - b + 1))*KummerM(a, b, z)+(GAMMA(b - 1))/(GAMMA(a))*(z)^(1 - b)* KummerM(a - b + 1, 2 - b, z) HypergeometricU[a, b, z]=Divide[Gamma[1 - b],Gamma[a - b + 1]]*Hypergeometric1F1[a, b, z]+Divide[Gamma[b - 1],Gamma[a]]*(z)^(1 - b)* Hypergeometric1F1[a - b + 1, 2 - b, z] Successful Successful - -
13.3.E1 (b - a)* KummerM(a - 1, b, z)+(2*a - b + z)* KummerM(a, b, z)- a*KummerM(a + 1, b, z)= 0 (b - a)* Hypergeometric1F1[a - 1, b, z]+(2*a - b + z)* Hypergeometric1F1[a, b, z]- a*Hypergeometric1F1[a + 1, b, z]= 0 Successful Successful - -
13.3.E2 b*(b - 1)* KummerM(a, b - 1, z)+ b*(1 - b - z)* KummerM(a, b, z)+ z*(b - a)* KummerM(a, b + 1, z)= 0 b*(b - 1)* Hypergeometric1F1[a, b - 1, z]+ b*(1 - b - z)* Hypergeometric1F1[a, b, z]+ z*(b - a)* Hypergeometric1F1[a, b + 1, z]= 0 Successful Successful - -
13.3.E3 (a - b + 1)* KummerM(a, b, z)- a*KummerM(a + 1, b, z)+(b - 1)* KummerM(a, b - 1, z)= 0 (a - b + 1)* Hypergeometric1F1[a, b, z]- a*Hypergeometric1F1[a + 1, b, z]+(b - 1)* Hypergeometric1F1[a, b - 1, z]= 0 Successful Successful - -
13.3.E4 b*KummerM(a, b, z)- b*KummerM(a - 1, b, z)- z*KummerM(a, b + 1, z)= 0 b*Hypergeometric1F1[a, b, z]- b*Hypergeometric1F1[a - 1, b, z]- z*Hypergeometric1F1[a, b + 1, z]= 0 Successful Successful - -
13.3.E5 b*(a + z)* KummerM(a, b, z)+ z*(a - b)* KummerM(a, b + 1, z)- a*b*KummerM(a + 1, b, z)= 0 b*(a + z)* Hypergeometric1F1[a, b, z]+ z*(a - b)* Hypergeometric1F1[a, b + 1, z]- a*b*Hypergeometric1F1[a + 1, b, z]= 0 Successful Successful - -
13.3.E6 (a - 1 + z)* KummerM(a, b, z)+(b - a)* KummerM(a - 1, b, z)+(1 - b)* KummerM(a, b - 1, z)= 0 (a - 1 + z)* Hypergeometric1F1[a, b, z]+(b - a)* Hypergeometric1F1[a - 1, b, z]+(1 - b)* Hypergeometric1F1[a, b - 1, z]= 0 Successful Successful - -
13.3.E7 KummerU(a - 1, b, z)+(b - 2*a - z)* KummerU(a, b, z)+ a*(a - b + 1)* KummerU(a + 1, b, z)= 0 HypergeometricU[a - 1, b, z]+(b - 2*a - z)* HypergeometricU[a, b, z]+ a*(a - b + 1)* HypergeometricU[a + 1, b, z]= 0 Successful Successful - -
13.3.E8 (b - a - 1)* KummerU(a, b - 1, z)+(1 - b - z)* KummerU(a, b, z)+ z*KummerU(a, b + 1, z)= 0 (b - a - 1)* HypergeometricU[a, b - 1, z]+(1 - b - z)* HypergeometricU[a, b, z]+ z*HypergeometricU[a, b + 1, z]= 0 Successful Successful - -
13.3.E9 KummerU(a, b, z)- a*KummerU(a + 1, b, z)- KummerU(a, b - 1, z)= 0 HypergeometricU[a, b, z]- a*HypergeometricU[a + 1, b, z]- HypergeometricU[a, b - 1, z]= 0 Successful Successful - -
13.3.E10 (b - a)* KummerU(a, b, z)+ KummerU(a - 1, b, z)- z*KummerU(a, b + 1, z)= 0 (b - a)* HypergeometricU[a, b, z]+ HypergeometricU[a - 1, b, z]- z*HypergeometricU[a, b + 1, z]= 0 Successful Successful - -
13.3.E11 (a + z)* KummerU(a, b, z)- z*KummerU(a, b + 1, z)+ a*(b - a - 1)* KummerU(a + 1, b, z)= 0 (a + z)* HypergeometricU[a, b, z]- z*HypergeometricU[a, b + 1, z]+ a*(b - a - 1)* HypergeometricU[a + 1, b, z]= 0 Successful Successful - -
13.3.E12 (a - 1 + z)* KummerU(a, b, z)- KummerU(a - 1, b, z)+(a - b + 1)* KummerU(a, b - 1, z)= 0 (a - 1 + z)* HypergeometricU[a, b, z]- HypergeometricU[a - 1, b, z]+(a - b + 1)* HypergeometricU[a, b - 1, z]= 0 Successful Successful - -
13.3.E13 (a + 1)* z*KummerM(a + 2, b + 2, z)+(b + 1)*(b - z)* KummerM(a + 1, b + 1, z)- b*(b + 1)* KummerM(a, b, z)= 0 (a + 1)* z*Hypergeometric1F1[a + 2, b + 2, z]+(b + 1)*(b - z)* Hypergeometric1F1[a + 1, b + 1, z]- b*(b + 1)* Hypergeometric1F1[a, b, z]= 0 Successful Successful - -
13.3.E14 (a + 1)* z*KummerU(a + 2, b + 2, z)+(z - b)* KummerU(a + 1, b + 1, z)- KummerU(a, b, z)= 0 (a + 1)* z*HypergeometricU[a + 2, b + 2, z]+(z - b)* HypergeometricU[a + 1, b + 1, z]- HypergeometricU[a, b, z]= 0 Successful Successful - -
13.3.E15 diff(KummerM(a, b, z), z)=(a)/(b)*KummerM(a + 1, b + 1, z) D[Hypergeometric1F1[a, b, z], z]=Divide[a,b]*Hypergeometric1F1[a + 1, b + 1, z] Successful Successful - -
13.3.E16 diff(KummerM(a, b, z), [z$(n)])=(pochhammer(a, n))/(pochhammer(b, n))*KummerM(a + n, b + n, z) D[Hypergeometric1F1[a, b, z], {z, n}]=Divide[Pochhammer[a, n],Pochhammer[b, n]]*Hypergeometric1F1[a + n, b + n, z] Successful Failure - Skip
13.3.E17 (z*diff(z, z))^(n)*((z)^(a - 1)* KummerM(a, b, z))= pochhammer(a, n)*(z)^(a + n - 1)* KummerM(a + n, b, z) (z*D[z, z])^(n)*((z)^(a - 1)* Hypergeometric1F1[a, b, z])= Pochhammer[a, n]*(z)^(a + n - 1)* Hypergeometric1F1[a + n, b, z] Failure Failure
Fail
2.537884887+11.89104377*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
-123.7627467+81.19826795*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
-1555.783365-1131.870657*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
-1.589608076+60.84364464*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
Skip
13.3.E18 diff((z)^(b - 1)* KummerM(a, b, z), [z$(n)])= pochhammer(b - n, n)*(z)^(b - n - 1)* KummerM(a, b - n, z) D[(z)^(b - 1)* Hypergeometric1F1[a, b, z], {z, n}]= Pochhammer[b - n, n]*(z)^(b - n - 1)* Hypergeometric1F1[a, b - n, z] Failure Failure Successful Skip
13.3.E19 (z*diff(z, z))^(n)*((z)^(b - a - 1)* exp(- z)*KummerM(a, b, z))= pochhammer(b - a, n)*(z)^(b - a + n - 1)* exp(- z)*KummerM(a - n, b, z) (z*D[z, z])^(n)*((z)^(b - a - 1)* Exp[- z]*Hypergeometric1F1[a, b, z])= Pochhammer[b - a, n]*(z)^(b - a + n - 1)* Exp[- z]*Hypergeometric1F1[a - n, b, z] Failure Failure
Fail
1.000000000+0.*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
1.414213562+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
0.+3.999999998*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
1.000000000+0.*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
Skip
13.3.E20 diff(exp(- z)*KummerM(a, b, z), [z$(n)])=(- 1)^(n)*(pochhammer(b - a, n))/(pochhammer(b, n))*exp(- z)*KummerM(a, b + n, z) D[Exp[- z]*Hypergeometric1F1[a, b, z], {z, n}]=(- 1)^(n)*Divide[Pochhammer[b - a, n],Pochhammer[b, n]]*Exp[- z]*Hypergeometric1F1[a, b + n, z] Failure Failure Successful Skip
13.3.E21 diff((z)^(b - 1)* exp(- z)*KummerM(a, b, z), [z$(n)])= pochhammer(b - n, n)*(z)^(b - n - 1)* exp(- z)*KummerM(a - n, b - n, z) D[(z)^(b - 1)* Exp[- z]*Hypergeometric1F1[a, b, z], {z, n}]= Pochhammer[b - n, n]*(z)^(b - n - 1)* Exp[- z]*Hypergeometric1F1[a - n, b - n, z] Failure Failure Skip Error
13.3.E22 diff(KummerU(a, b, z), z)= - a*KummerU(a + 1, b + 1, z) D[HypergeometricU[a, b, z], z]= - a*HypergeometricU[a + 1, b + 1, z] Successful Successful - -
13.3.E23 diff(KummerU(a, b, z), [z$(n)])=(- 1)^(n)* pochhammer(a, n)*KummerU(a + n, b + n, z) D[HypergeometricU[a, b, z], {z, n}]=(- 1)^(n)* Pochhammer[a, n]*HypergeometricU[a + n, b + n, z] Failure Successful Skip -
13.3.E24 (z*diff(z, z))^(n)*((z)^(a - 1)* KummerU(a, b, z))= pochhammer(a, n)*pochhammer(a - b + 1, n)*(z)^(a + n - 1)* KummerU(a + n, b, z) (z*D[z, z])^(n)*((z)^(a - 1)* HypergeometricU[a, b, z])= Pochhammer[a, n]*Pochhammer[a - b + 1, n]*(z)^(a + n - 1)* HypergeometricU[a + n, b, z] Failure Failure
Fail
.3178044521-.5812355890e-1*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
.5638915996+.3833395878*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
.2833587160+.898459259*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
.2659178351-.5754539144*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
Skip
13.3.E25 diff((z)^(b - 1)* KummerU(a, b, z), [z$(n)])=(- 1)^(n)* pochhammer(a - b + 1, n)*(z)^(b - n - 1)* KummerU(a, b - n, z) D[(z)^(b - 1)* HypergeometricU[a, b, z], {z, n}]=(- 1)^(n)* Pochhammer[a - b + 1, n]*(z)^(b - n - 1)* HypergeometricU[a, b - n, z] Failure Failure Skip Skip
13.3.E26 (z*diff(z, z))^(n)*((z)^(b - a - 1)* exp(- z)*KummerU(a, b, z))=(- 1)^(n)* (z)^(b - a + n - 1)* exp(- z)*KummerU(a - n, b, z) (z*D[z, z])^(n)*((z)^(b - a - 1)* Exp[- z]*HypergeometricU[a, b, z])=(- 1)^(n)* (z)^(b - a + n - 1)* Exp[- z]*HypergeometricU[a - n, b, z] Failure Failure
Fail
-.6426838098-.1638932643*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
-2.885602225+1.867279788*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
-8.024434137+19.17405510*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
.5784828818e-1+.5986041895e-1*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
Skip
13.3.E27 diff(exp(- z)*KummerU(a, b, z), [z$(n)])=(- 1)^(n)* exp(- z)*KummerU(a, b + n, z) D[Exp[- z]*HypergeometricU[a, b, z], {z, n}]=(- 1)^(n)* Exp[- z]*HypergeometricU[a, b + n, z] Failure Failure Skip Skip
13.3.E28 diff((z)^(b - 1)* exp(- z)*KummerU(a, b, z), [z$(n)])=(- 1)^(n)* (z)^(b - n - 1)* exp(- z)*KummerU(a - n, b - n, z) D[(z)^(b - 1)* Exp[- z]*HypergeometricU[a, b, z], {z, n}]=(- 1)^(n)* (z)^(b - n - 1)* Exp[- z]*HypergeometricU[a - n, b - n, z] Error Failure - Error
13.3.E29 (z*diff(z, z))^(n)= (z)^(n)* diff((z)^(n), [z$(n)]) (z*D[z, z])^(n)= (z)^(n)* D[(z)^(n), {z, n}] Failure Failure
Fail
28.28427122-28.28427122*I <- {z = 2^(1/2)+I*2^(1/2), n = 3}
28.28427122+28.28427122*I <- {z = 2^(1/2)-I*2^(1/2), n = 3}
-28.28427122+28.28427122*I <- {z = -2^(1/2)-I*2^(1/2), n = 3}
-28.28427122-28.28427122*I <- {z = -2^(1/2)+I*2^(1/2), n = 3}
Fail
Complex[28.284271247461902, -28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[28.284271247461902, 28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-28.284271247461902, 28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-28.284271247461902, -28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
13.4.E1 KummerM(a, b, z)/GAMMA(b)=(1)/(GAMMA(a)*GAMMA(b - a))*int(exp(z*t)*(t)^(a - 1)*(1 - t)^(b - a - 1), t = 0..1) Hypergeometric1F1Regularized[a, b, z]=Divide[1,Gamma[a]*Gamma[b - a]]*Integrate[Exp[z*t]*(t)^(a - 1)*(1 - t)^(b - a - 1), {t, 0, 1}] Successful Failure - Skip
13.4.E2 KummerM(a, b, z)/GAMMA(b)=(1)/(GAMMA(b - c))*int(KummerM(a, c, z*t)/GAMMA(c)*(t)^(c - 1)*(1 - t)^(b - c - 1), t = 0..1) Hypergeometric1F1Regularized[a, b, z]=Divide[1,Gamma[b - c]]*Integrate[Hypergeometric1F1Regularized[a, c, z*t]*(t)^(c - 1)*(1 - t)^(b - c - 1), {t, 0, 1}] Successful Failure - Skip
13.4.E3 KummerM(a, b, - z)/GAMMA(b)=((z)^((1)/(2)-(1)/(2)*b))/(GAMMA(a))*int(exp(- t)*(t)^(a -(1)/(2)*b -(1)/(2))* BesselJ(b - 1, 2*sqrt(z*t)), t = 0..infinity) Hypergeometric1F1Regularized[a, b, - z]=Divide[(z)^(Divide[1,2]-Divide[1,2]*b),Gamma[a]]*Integrate[Exp[- t]*(t)^(a -Divide[1,2]*b -Divide[1,2])* BesselJ[b - 1, 2*Sqrt[z*t]], {t, 0, Infinity}] Failure Failure Skip Error
13.4.E4 KummerU(a, b, z)=(1)/(GAMMA(a))*int(exp(- z*t)*(t)^(a - 1)*(1 + t)^(b - a - 1), t = 0..infinity) HypergeometricU[a, b, z]=Divide[1,Gamma[a]]*Integrate[Exp[- z*t]*(t)^(a - 1)*(1 + t)^(b - a - 1), {t, 0, Infinity}] Successful Failure - Error
13.4.E5 KummerU(a, b, z)=((z)^(1 - a))/(GAMMA(a)*GAMMA(1 + a - b))*int((KummerU(b - a, b, t)*exp(- t)*(t)^(a - 1))/(t + z), t = 0..infinity) HypergeometricU[a, b, z]=Divide[(z)^(1 - a),Gamma[a]*Gamma[1 + a - b]]*Integrate[Divide[HypergeometricU[b - a, b, t]*Exp[- t]*(t)^(a - 1),t + z], {t, 0, Infinity}] Failure Failure Skip Error
13.4.E6 KummerU(a, b, z)=((- 1)^(n)* (z)^(1 - b - n))/(GAMMA(1 + a - b))*int((KummerM(b - a, b, t)/GAMMA(b)*exp(- t)*(t)^(b + n - 1))/(t + z), t = 0..infinity) HypergeometricU[a, b, z]=Divide[(- 1)^(n)* (z)^(1 - b - n),Gamma[1 + a - b]]*Integrate[Divide[Hypergeometric1F1Regularized[b - a, b, t]*Exp[- t]*(t)^(b + n - 1),t + z], {t, 0, Infinity}] Failure Failure Skip Error
13.4.E7 KummerU(a, b, z)=(2*(z)^((1)/(2)-(1)/(2)*b))/(GAMMA(a)*GAMMA(a - b + 1))* int(exp(- t)*(t)^(a -(1)/(2)*b -(1)/(2))* BesselK(b - 1, 2*sqrt(z*t)), t = 0..infinity) HypergeometricU[a, b, z]=Divide[2*(z)^(Divide[1,2]-Divide[1,2]*b),Gamma[a]*Gamma[a - b + 1]]* Integrate[Exp[- t]*(t)^(a -Divide[1,2]*b -Divide[1,2])* BesselK[b - 1, 2*Sqrt[z*t]], {t, 0, Infinity}] Successful Failure - Error
13.4.E8 KummerU(a, b, z)= (z)^(c - a)* int(exp(- z*t)*(t)^(c - 1)* hypergeom([a , a - b + 1], [c], - t), t = 0..infinity) HypergeometricU[a, b, z]= (z)^(c - a)* Integrate[Exp[- z*t]*(t)^(c - 1)* HypergeometricPFQRegularized[{a , a - b + 1}, {c}, - t], {t, 0, Infinity}] Failure Failure Skip Error
13.4.E9 KummerM(a, b, z)/GAMMA(b)=(GAMMA(1 + a - b))/(2*Pi*I*GAMMA(a))*int(exp(z*t)*(t)^(a - 1)*(t - 1)^(b - a - 1), t = 0..(1 +)) Hypergeometric1F1Regularized[a, b, z]=Divide[Gamma[1 + a - b],2*Pi*I*Gamma[a]]*Integrate[Exp[z*t]*(t)^(a - 1)*(t - 1)^(b - a - 1), {t, 0, (1 +)}] Error Failure - Error
13.4.E10 KummerM(a, b, z)/GAMMA(b)= exp(- a*Pi*I)*(GAMMA(1 - a))/(2*Pi*I*GAMMA(b - a))*int(exp(z*t)*(t)^(a - 1)*(1 - t)^(b - a - 1), t = 1..(0 +)) Hypergeometric1F1Regularized[a, b, z]= Exp[- a*Pi*I]*Divide[Gamma[1 - a],2*Pi*I*Gamma[b - a]]*Integrate[Exp[z*t]*(t)^(a - 1)*(1 - t)^(b - a - 1), {t, 1, (0 +)}] Error Failure - Error
13.4.E11 KummerM(a, b, z)/GAMMA(b)= exp(- b*Pi*I)*GAMMA(1 - a)*GAMMA(1 + a - b)*(1)/(4*(Pi)^(2))*int(exp(z*t)*(t)^(a - 1)*(1 - t)^(b - a - 1), t = alpha..(0 + , 1 + , 0 - , 1 -)) Hypergeometric1F1Regularized[a, b, z]= Exp[- b*Pi*I]*Gamma[1 - a]*Gamma[1 + a - b]*Divide[1,4*(Pi)^(2)]*Integrate[Exp[z*t]*(t)^(a - 1)*(1 - t)^(b - a - 1), {t, \[Alpha], (0 + , 1 + , 0 - , 1 -)}] Error Failure - Error
13.4.E12 KummerM(a, c, z)/GAMMA(c)=(GAMMA(b))/(2*Pi*I)*(z)^(1 - b)* int(exp(z*t)*(t)^(- b)* hypergeom([a , b], [c], (1)/(t)), t = - infinity..(0 + , 1 +)) Hypergeometric1F1Regularized[a, c, z]=Divide[Gamma[b],2*Pi*I]*(z)^(1 - b)* Integrate[Exp[z*t]*(t)^(- b)* HypergeometricPFQRegularized[{a , b}, {c}, Divide[1,t]], {t, - Infinity, (0 + , 1 +)}] Error Failure - Error
13.4.E13 KummerM(a, b, z)/GAMMA(b)=((z)^(1 - b))/(2*Pi*I)*int(exp(z*t)*(t)^(- b)*(1 -(1)/(t))^(- a), t = - infinity..(0 + , 1 +)) Hypergeometric1F1Regularized[a, b, z]=Divide[(z)^(1 - b),2*Pi*I]*Integrate[Exp[z*t]*(t)^(- b)*(1 -Divide[1,t])^(- a), {t, - Infinity, (0 + , 1 +)}] Error Failure - Error
13.4.E14 KummerU(a, b, z)= exp(- a*Pi*I)*(GAMMA(1 - a))/(2*Pi*I)*int(exp(- z*t)*(t)^(a - 1)*(1 + t)^(b - a - 1), t = infinity..(0 +)) HypergeometricU[a, b, z]= Exp[- a*Pi*I]*Divide[Gamma[1 - a],2*Pi*I]*Integrate[Exp[- z*t]*(t)^(a - 1)*(1 + t)^(b - a - 1), {t, Infinity, (0 +)}] Error Failure - Error
13.4.E15 (KummerU(a, b, z))/(GAMMA(c)*GAMMA(c - b + 1))=((z)^(1 - c))/(2*Pi*I)*int(exp(z*t)*(t)^(- c)* hypergeom([a , c], [a + c - b + 1], 1 -(1)/(t)), t = - infinity..(0 +)) Divide[HypergeometricU[a, b, z],Gamma[c]*Gamma[c - b + 1]]=Divide[(z)^(1 - c),2*Pi*I]*Integrate[Exp[z*t]*(t)^(- c)* HypergeometricPFQRegularized[{a , c}, {a + c - b + 1}, 1 -Divide[1,t]], {t, - Infinity, (0 +)}] Error Failure - Error
13.4.E16 KummerM(a, b, - z)/GAMMA(b)=(1)/(2*Pi*I*GAMMA(a))*int((GAMMA(a + t)*GAMMA(- t))/(GAMMA(b + t))*(z)^(t), t = - I*infinity..I*infinity) Hypergeometric1F1Regularized[a, b, - z]=Divide[1,2*Pi*I*Gamma[a]]*Integrate[Divide[Gamma[a + t]*Gamma[- t],Gamma[b + t]]*(z)^(t), {t, - I*Infinity, I*Infinity}] Failure Failure Skip Error
13.4.E17 KummerU(a, b, z)=((z)^(- a))/(2*Pi*I)*int((GAMMA(a + t)*GAMMA(1 + a - b + t)*GAMMA(- t))/(GAMMA(a)*GAMMA(1 + a - b))*(z)^(- t), t = - I*infinity..I*infinity) HypergeometricU[a, b, z]=Divide[(z)^(- a),2*Pi*I]*Integrate[Divide[Gamma[a + t]*Gamma[1 + a - b + t]*Gamma[- t],Gamma[a]*Gamma[1 + a - b]]*(z)^(- t), {t, - I*Infinity, I*Infinity}] Failure Failure Skip Error
13.4.E18 KummerU(a, b, z)=((z)^(1 - b)* exp(z))/(2*Pi*I)*int((GAMMA(b - 1 + t)*GAMMA(t))/(GAMMA(a + t))*(z)^(- t), t = - I*infinity..I*infinity) HypergeometricU[a, b, z]=Divide[(z)^(1 - b)* Exp[z],2*Pi*I]*Integrate[Divide[Gamma[b - 1 + t]*Gamma[t],Gamma[a + t]]*(z)^(- t), {t, - I*Infinity, I*Infinity}] Failure Failure Skip Error
13.6.E1 KummerM(a, a, z)= exp(z) Hypergeometric1F1[a, a, z]= Exp[z] Successful Successful - -
13.6.E2 KummerM(1, 2, 2*z)=(exp(z))/(z)*sinh(z) Hypergeometric1F1[1, 2, 2*z]=Divide[Exp[z],z]*Sinh[z] Successful Successful - -
13.6.E3 KummerM(0, b, z)= KummerU(0, b, z) Hypergeometric1F1[0, b, z]= HypergeometricU[0, b, z] Successful Successful - -
13.6.E3 KummerU(0, b, z)= 1 HypergeometricU[0, b, z]= 1 Successful Successful - -
13.6.E4 KummerU(a, a + 1, z)= (z)^(- a) HypergeometricU[a, a + 1, z]= (z)^(- a) Failure Successful Successful -
13.6.E5