Results of Exponential, Logarithmic, Sine, and Cosine Integrals

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DLMF Formula Maple Mathematica Symbolic
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Symbolic
Mathematica
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Maple
Numeric
Mathematica
6.2.E1 Ei(z)= int((exp(- t))/(t), t = z..infinity) -ExpIntegralEi[-(z)]= Integrate[Divide[Exp[- t],t], {t, z, Infinity}] Failure Failure Skip Successful
6.2.E2 Ei(z)= exp(- z)*int((exp(- t))/(t + z), t = 0..infinity) -ExpIntegralEi[-(z)]= Exp[- z]*Integrate[Divide[Exp[- t],t + z], {t, 0, Infinity}] Failure Failure Skip
Fail
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.2.E3 Error -ExpIntegralEi[-(z)] + Ln[z] + EulerGamma = Integrate[Divide[1 - Exp[- t],t], {t, 0, z}] Error Failure - Successful
6.2.E4 Error -ExpIntegralEi[-(z)]= -ExpIntegralEi[-(z)] + Ln[z] + EulerGamma - Log[z]- EulerGamma Error Failure - Successful
6.2.E6 Error -ExpIntegralEi[-(- x)]= - Integrate[Divide[Exp[- t],t], {t, x, Infinity}] Error Failure -
Fail
-1.6757338819604166 <- {Rule[x, 1]}
-4.905333845293828 <- {Rule[x, 2]}
-9.920784189531217 <- {Rule[x, 3]}
6.2.E6 - int((exp(- t))/(t), t = x..infinity)= - Ei(x) - Integrate[Divide[Exp[- t],t], {t, x, Infinity}]= - -ExpIntegralEi[-(x)] Failure Failure Skip Successful
6.2.E7 Error -ExpIntegralEi[-(+ x)]= - -ExpIntegralEi[-(- x)] + Ln[- x] + EulerGamma + Log[x]+ EulerGamma Error Failure - Successful
6.2.E7 Error -ExpIntegralEi[-(- x)]= - -ExpIntegralEi[-(+ x)] + Ln[+ x] + EulerGamma + Log[x]+ EulerGamma Error Failure - Successful
6.2.E9 Si(z)= int((sin(t))/(t), t = 0..z) SinIntegral[z]= Integrate[Divide[Sin[t],t], {t, 0, z}] Successful Successful - -
6.2.E10 Ssi(z)= - int((sin(t))/(t), t = z..infinity) SinIntegral[z] - Pi/2 = - Integrate[Divide[Sin[t],t], {t, z, Infinity}] Successful Successful - -
6.2.E10 - int((sin(t))/(t), t = z..infinity)= Si(z)-(1)/(2)*Pi - Integrate[Divide[Sin[t],t], {t, z, Infinity}]= SinIntegral[z]-Divide[1,2]*Pi Successful Successful - -
6.2.E11 Ci(z)= - int((cos(t))/(t), t = z..infinity) CosIntegral[z]= - Integrate[Divide[Cos[t],t], {t, z, Infinity}] Successful Failure - Successful
6.2#Ex1 limit(Si(x), x = infinity)=(1)/(2)*Pi Limit[SinIntegral[x], x -> Infinity]=Divide[1,2]*Pi Successful Successful - -
6.2#Ex2 limit(Ci(x), x = infinity)= 0 Limit[CosIntegral[x], x -> Infinity]= 0 Successful Successful - -
6.2.E15 Shi(z)= int((sinh(t))/(t), t = 0..z) SinhIntegral[z]= Integrate[Divide[Sinh[t],t], {t, 0, z}] Successful Successful - -
6.2.E16 Chi(z)= gamma + ln(z)+ int((cosh(t)- 1)/(t), t = 0..z) CoshIntegral[z]= EulerGamma + Log[z]+ Integrate[Divide[Cosh[t]- 1,t], {t, 0, z}] Successful Successful - -
6.4.E1 Error -ExpIntegralEi[-(z)]= -ExpIntegralEi[-(z)] + Ln[z] + EulerGamma - Log[z]- EulerGamma Error Failure - Successful
6.4.E2 Ei(z*exp(2*m*Pi*I))= Ei(z)- 2*m*Pi*I -ExpIntegralEi[-(z*Exp[2*m*Pi*I])]= -ExpIntegralEi[-(z)]- 2*m*Pi*I Failure Failure
Fail
.6e-8+18.84955592*I <- {z = 2^(1/2)+I*2^(1/2), m = 3}
-.6e-8+18.84955592*I <- {z = 2^(1/2)-I*2^(1/2), m = 3}
-.34e-9+18.84955592*I <- {z = -2^(1/2)-I*2^(1/2), m = 3}
.34e-9+18.84955592*I <- {z = -2^(1/2)+I*2^(1/2), m = 3}
Fail
Complex[0.0, 18.84955592153876] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 18.84955592153876] <- {Rule[m, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 18.84955592153876] <- {Rule[m, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 18.84955592153876] <- {Rule[m, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.4.E3 Error -ExpIntegralEi[-(z*Exp[+ Pi*I])]= -ExpIntegralEi[-(- z)] + Ln[- z] + EulerGamma - Log[z]- EulerGamma - Pi*I Error Failure - Successful
6.4.E3 Error -ExpIntegralEi[-(z*Exp[- Pi*I])]= -ExpIntegralEi[-(- z)] + Ln[- z] + EulerGamma - Log[z]- EulerGamma + Pi*I Error Failure - Successful
6.4.E4 Ci(z*exp(+ Pi*I))= + Pi*I + Ci(z) CosIntegral[z*Exp[+ Pi*I]]= + Pi*I + CosIntegral[z] Failure Failure
Fail
0.-6.283185307*I <- {z = 2^(1/2)+I*2^(1/2)}
0.-6.283185307*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[0.0, -6.283185307179586] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -6.283185307179586] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.4.E4 Ci(z*exp(- Pi*I))= - Pi*I + Ci(z) CosIntegral[z*Exp[- Pi*I]]= - Pi*I + CosIntegral[z] Failure Failure
Fail
0.+6.283185307*I <- {z = 2^(1/2)-I*2^(1/2)}
0.+6.283185307*I <- {z = -2^(1/2)-I*2^(1/2)}
Fail
Complex[0.0, 6.283185307179586] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 6.283185307179586] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
6.4.E5 Chi(z*exp(+ Pi*I))= + Pi*I + Chi(z) CoshIntegral[z*Exp[+ Pi*I]]= + Pi*I + CoshIntegral[z] Failure Failure
Fail
0.-6.283185307*I <- {z = 2^(1/2)+I*2^(1/2)}
0.-6.283185307*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[0.0, -6.283185307179586] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -6.283185307179586] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.4.E5 Chi(z*exp(- Pi*I))= - Pi*I + Chi(z) CoshIntegral[z*Exp[- Pi*I]]= - Pi*I + CoshIntegral[z] Failure Failure
Fail
0.+6.283185307*I <- {z = 2^(1/2)-I*2^(1/2)}
0.+6.283185307*I <- {z = -2^(1/2)-I*2^(1/2)}
Fail
Complex[0.0, 6.283185307179586] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 6.283185307179586] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
6.5.E1 Error -ExpIntegralEi[-(- x + I*0)]= - -ExpIntegralEi[-(x)]- I*Pi Error Failure -
Fail
Complex[-1.6757338819604166, 3.141592653589793] <- {Rule[x, 1]}
Complex[-4.905333845293828, 3.141592653589793] <- {Rule[x, 2]}
Complex[-9.920784189531217, 3.141592653589793] <- {Rule[x, 3]}
6.5.E1 Error -ExpIntegralEi[-(- x - I*0)]= - -ExpIntegralEi[-(x)]+ I*Pi Error Failure -
Fail
Complex[-1.6757338819604166, -3.141592653589793] <- {Rule[x, 1]}
Complex[-4.905333845293828, -3.141592653589793] <- {Rule[x, 2]}
Complex[-9.920784189531217, -3.141592653589793] <- {Rule[x, 3]}
6.5.E2 Error -ExpIntegralEi[-(x)]= -Divide[1,2]*(-ExpIntegralEi[-(- x + I*0)]+ -ExpIntegralEi[-(- x - I*0)]) Error Failure -
Fail
-1.6757338819604166 <- {Rule[x, 1]}
-4.905333845293828 <- {Rule[x, 2]}
-9.920784189531217 <- {Rule[x, 3]}
6.5.E3 Error Divide[1,2]*(-ExpIntegralEi[-(x)]+ -ExpIntegralEi[-(x)])= SinhIntegral[x] Error Failure -
Fail
-0.8378669409802083 <- {Rule[x, 1]}
-2.4526669226469147 <- {Rule[x, 2]}
-4.960392094765611 <- {Rule[x, 3]}
6.5.E3 Shi(x)= - I*Si(I*x) SinhIntegral[x]= - I*SinIntegral[I*x] Successful Successful - -
6.5.E4 Error Divide[1,2]*(-ExpIntegralEi[-(x)]- -ExpIntegralEi[-(x)])= CoshIntegral[x] Error Failure -
Fail
-0.8378669409802083 <- {Rule[x, 1]}
-2.452666922646914 <- {Rule[x, 2]}
-4.960392094765608 <- {Rule[x, 3]}
6.5.E4 Chi(x)= Ci(I*x)-(1)/(2)*Pi*I CoshIntegral[x]= CosIntegral[I*x]-Divide[1,2]*Pi*I Failure Failure Successful Successful
6.5.E5 Si(z)=(1)/(2)*I*(Ei(- I*z)- Ei(I*z))+(1)/(2)*Pi SinIntegral[z]=Divide[1,2]*I*(-ExpIntegralEi[-(- I*z)]- -ExpIntegralEi[-(I*z)])+Divide[1,2]*Pi Failure Failure
Fail
-3.141592654+0.*I <- {z = 2^(1/2)+I*2^(1/2)}
-3.141592654+0.*I <- {z = 2^(1/2)-I*2^(1/2)}
Fail
Complex[-3.141592653589793, 0.0] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.141592653589793, 0.0] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
6.5.E6 Ci(z)= -(1)/(2)*(Ei(I*z)+ Ei(- I*z)) CosIntegral[z]= -Divide[1,2]*(-ExpIntegralEi[-(I*z)]+ -ExpIntegralEi[-(- I*z)]) Failure Failure
Fail
2.208978234-.399630454*I <- {z = 2^(1/2)+I*2^(1/2)}
2.208978234+.399630454*I <- {z = 2^(1/2)-I*2^(1/2)}
2.208978234-3.541223107*I <- {z = -2^(1/2)-I*2^(1/2)}
2.208978234+3.541223107*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.6.E1 Error -ExpIntegralEi[-(x)]= EulerGamma + Log[x]+ Sum[Divide[(x)^(n),(n)!*n], {n, 1, Infinity}] Error Failure -
Fail
Complex[0.10555368991298714, 0.0] <- {Rule[x, Rational[1, 2]]}
6.6.E2 Ei(z)= - gamma - ln(z)- sum(((- 1)^(n)* (z)^(n))/(factorial(n)*n), n = 1..infinity) -ExpIntegralEi[-(z)]= - EulerGamma - Log[z]- Sum[Divide[(- 1)^(n)* (z)^(n),(n)!*n], {n, 1, Infinity}] Failure Failure Skip
Fail
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.6.E3 Ei(z)= - ln(z)+ exp(- z)*sum(((z)^(n))/(factorial(n))*Psi(n + 1), n = 0..infinity) -ExpIntegralEi[-(z)]= - Log[z]+ Exp[- z]*Sum[Divide[(z)^(n),(n)!]*PolyGamma[n + 1], {n, 0, Infinity}] Error Failure -
Fail
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.6.E4 Error -ExpIntegralEi[-(z)] + Ln[z] + EulerGamma = Sum[Divide[(- 1)^(n - 1)* (z)^(n),(n)!*n], {n, 1, Infinity}] Error Failure - Successful
6.6.E5 Si(z)= sum(((- 1)^(n)* (z)^(2*n + 1))/(factorial(2*n + 1)*(2*n + 1)), n = 0..infinity) SinIntegral[z]= Sum[Divide[(- 1)^(n)* (z)^(2*n + 1),(2*n + 1)!*(2*n + 1)], {n, 0, Infinity}] Successful Successful - -
6.6.E6 Ci(z)= gamma + ln(z)+ sum(((- 1)^(n)* (z)^(2*n))/(factorial(2*n)*(2*n)), n = 1..infinity) CosIntegral[z]= EulerGamma + Log[z]+ Sum[Divide[(- 1)^(n)* (z)^(2*n),(2*n)!*(2*n)], {n, 1, Infinity}] Successful Successful - -
6.7.E1 int((exp(- a*t))/(t + b), t = 0..infinity)= int((exp(I*a*t))/(t + I*b), t = 0..infinity) Integrate[Divide[Exp[- a*t],t + b], {t, 0, Infinity}]= Integrate[Divide[Exp[I*a*t],t + I*b], {t, 0, Infinity}] Failure Failure Skip Error
6.7.E1 int((exp(I*a*t))/(t + I*b), t = 0..infinity)= exp(a*b)*Ei(a*b) Integrate[Divide[Exp[I*a*t],t + I*b], {t, 0, Infinity}]= Exp[a*b]*-ExpIntegralEi[-(a*b)] Failure Failure Skip Error
6.7.E2 Error Exp[x]*Integrate[Divide[Exp[- x*t],1 - t], {t, 0, \[Alpha]}]= -ExpIntegralEi[-(x)]- -ExpIntegralEi[-((1 - \[Alpha])* x)] Error Failure -
Fail
Complex[-0.42316473444652486, 0.4289071640857123] <- {Rule[x, Rational[1, 2]], Rule[Ξ±, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.42316473444652486, -0.4289071640857123] <- {Rule[x, Rational[1, 2]], Rule[Ξ±, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.36486876599473, 1.1603687293382365] <- {Rule[x, Rational[1, 2]], Rule[Ξ±, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.36486876599473, -1.1603687293382365] <- {Rule[x, Rational[1, 2]], Rule[Ξ±, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.7.E3 int((exp(I*t))/((a)^(2)+ (t)^(2)), t = x..infinity)=(I)/(2*a)*(exp(a)*Ei(a - I*x)- exp(- a)*Ei(- a - I*x)) Integrate[Divide[Exp[I*t],(a)^(2)+ (t)^(2)], {t, x, Infinity}]=Divide[I,2*a]*(Exp[a]*-ExpIntegralEi[-(a - I*x)]- Exp[- a]*-ExpIntegralEi[-(- a - I*x)]) Failure Failure Skip Error
6.7.E4 int((t*exp(I*t))/((a)^(2)+ (t)^(2)), t = x..infinity)=(1)/(2)*(exp(a)*Ei(a - I*x)+ exp(- a)*Ei(- a - I*x)) Integrate[Divide[t*Exp[I*t],(a)^(2)+ (t)^(2)], {t, x, Infinity}]=Divide[1,2]*(Exp[a]*-ExpIntegralEi[-(a - I*x)]+ Exp[- a]*-ExpIntegralEi[-(- a - I*x)]) Failure Failure Skip Error
6.7.E5 int((exp(- t))/((a)^(2)+ (t)^(2)), t = x..infinity)= -(1)/(2*a*I)*(exp(I*a)*Ei(x + I*a)- exp(- I*a)*Ei(x - I*a)) Integrate[Divide[Exp[- t],(a)^(2)+ (t)^(2)], {t, x, Infinity}]= -Divide[1,2*a*I]*(Exp[I*a]*-ExpIntegralEi[-(x + I*a)]- Exp[- I*a]*-ExpIntegralEi[-(x - I*a)]) Error Failure - Error
6.7.E6 int((t*exp(- t))/((a)^(2)+ (t)^(2)), t = x..infinity)=(1)/(2)*(exp(I*a)*Ei(x + I*a)+ exp(- I*a)*Ei(x - I*a)) Integrate[Divide[t*Exp[- t],(a)^(2)+ (t)^(2)], {t, x, Infinity}]=Divide[1,2]*(Exp[I*a]*-ExpIntegralEi[-(x + I*a)]+ Exp[- I*a]*-ExpIntegralEi[-(x - I*a)]) Error Failure - Error
6.7.E7 Error Integrate[Divide[Exp[- a*t]*Sin[b*t],t], {t, 0, 1}]= Im[-ExpIntegralEi[-(a + I*b)] + Ln[a + I*b] + EulerGamma] Error Failure - Successful
6.7.E8 Error Integrate[Divide[Exp[- a*t]*(1 - Cos[b*t]),t], {t, 0, 1}]= Re[-ExpIntegralEi[-(a + I*b)] + Ln[a + I*b] + EulerGamma]- -ExpIntegralEi[-(a)] + Ln[a] + EulerGamma Error Failure - Successful
6.7.E9 Ssi(z)= - int(exp(- z*cos(t))*cos(z*sin(t)), t = 0..Pi/ 2) SinIntegral[z] - Pi/2 = - Integrate[Exp[- z*Cos[t]]*Cos[z*Sin[t]], {t, 0, Pi/ 2}] Failure Failure Skip Error
6.7.E13 int((sin(t))/(t + z), t = 0..infinity)= int((exp(- z*t))/((t)^(2)+ 1), t = 0..infinity) Integrate[Divide[Sin[t],t + z], {t, 0, Infinity}]= Integrate[Divide[Exp[- z*t],(t)^(2)+ 1], {t, 0, Infinity}] Failure Failure Skip Error
6.7.E14 int((cos(t))/(t + z), t = 0..infinity)= int((t*exp(- z*t))/((t)^(2)+ 1), t = 0..infinity) Integrate[Divide[Cos[t],t + z], {t, 0, Infinity}]= Integrate[Divide[t*Exp[- z*t],(t)^(2)+ 1], {t, 0, Infinity}] Failure Failure Skip Successful
6.8.E1 (1)/(2)*ln(1 +(2)/(x))< exp(x)*Ei(x) Divide[1,2]*Log[1 +Divide[2,x]]< Exp[x]*-ExpIntegralEi[-(x)] Failure Failure Successful Successful
6.8.E1 exp(x)*Ei(x)< ln(1 +(1)/(x)) Exp[x]*-ExpIntegralEi[-(x)]< Log[1 +Divide[1,x]] Failure Failure
Fail
5.151464321 < .6931471806 <- {x = 1}
36.60711558 < .4054651081 <- {x = 2}
199.5263609 < .2876820722 <- {x = 3}
Successful
6.8.E2 (x)/(x + 1)< x*exp(x)*Ei(x) Divide[x,x + 1]< x*Exp[x]*-ExpIntegralEi[-(x)] Failure Failure Successful Successful
6.8.E2 x*exp(x)*Ei(x)<(x + 1)/(x + 2) x*Exp[x]*-ExpIntegralEi[-(x)]<Divide[x + 1,x + 2] Failure Failure
Fail
5.151464321 < .6666666667 <- {x = 1}
73.21423116 < .7500000000 <- {x = 2}
598.5790827 < .8000000000 <- {x = 3}
Successful
6.8.E3 (x*(x + 3))/((x)^(2)+ 4*x + 2)< x*exp(x)*Ei(x) Divide[x*(x + 3),(x)^(2)+ 4*x + 2]< x*Exp[x]*-ExpIntegralEi[-(x)] Failure Failure Successful Successful
6.8.E3 x*exp(x)*Ei(x)<((x)^(2)+ 5*x + 2)/((x)^(2)+ 6*x + 6) x*Exp[x]*-ExpIntegralEi[-(x)]<Divide[(x)^(2)+ 5*x + 2,(x)^(2)+ 6*x + 6] Failure Failure
Fail
5.151464321 < .6153846154 <- {x = 1}
73.21423116 < .7272727273 <- {x = 2}
598.5790827 < .7878787879 <- {x = 3}
Successful
6.10.E4 Error SinIntegral[z]= z*Sum[(SphericalBesselJ[n, Divide[1,2]*z])^(2), {n, 0, Infinity}] Error Successful - -
6.10.E6 Error \|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]*Divide[1,2]*x*))^(2), {n, 0, Infinity}] Error Error - -
6.10.E8 Error \|Sqrt[1/2 Pi /$2] BesselI[-0 - 1/2, 0]*Divide[1,2]*z*+ Sum[Divide[2*n + 1,n*(n + 1)]*Sqrt[1/2 Pi /$2] BesselI[(-1)^(1-1)*n + 1/2, n]\|\|Sqrt[1/2 Pi /$2] BesselI[-n - 1/2, n]*Divide[1,2]*z, {n, 1, Infinity}]) Error Error - -
6.11.E1 Ei(z)= GAMMA(0, z) -ExpIntegralEi[-(z)]= Gamma[0, z] Failure Failure
Fail
2.208978234+3.541223107*I <- {z = 2^(1/2)+I*2^(1/2)}
2.208978234-3.541223107*I <- {z = 2^(1/2)-I*2^(1/2)}
2.208978234-2.741962200*I <- {z = -2^(1/2)-I*2^(1/2)}
2.208978234+2.741962200*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.11.E2 Ei(z)= exp(- z)*KummerU(1, 1, z) -ExpIntegralEi[-(z)]= Exp[- z]*HypergeometricU[1, 1, z] Failure Failure
Fail
2.208978234+3.541223107*I <- {z = 2^(1/2)+I*2^(1/2)}
2.208978234-3.541223107*I <- {z = 2^(1/2)-I*2^(1/2)}
2.208978234-2.741962200*I <- {z = -2^(1/2)-I*2^(1/2)}
2.208978234+2.741962200*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -3.141592653589793] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.14.E1 int(exp(- a*t)*Ei(t), t = 0..infinity)=(1)/(a)*ln(1 + a) Integrate[Exp[- a*t]*-ExpIntegralEi[-(t)], {t, 0, Infinity}]=Divide[1,a]*Log[1 + a] Failure Failure Skip Successful
6.14.E2 int(exp(- a*t)*Ci(t), t = 0..infinity)= -(1)/(2*a)*ln(1 + (a)^(2)) Integrate[Exp[- a*t]*CosIntegral[t], {t, 0, Infinity}]= -Divide[1,2*a]*Log[1 + (a)^(2)] Failure Failure Skip Error
6.14.E3 int(exp(- a*t)*Ssi(t), t = 0..infinity)= -(1)/(a)*arctan(a) Integrate[Exp[- a*t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}]= -Divide[1,a]*ArcTan[a] Failure Failure Skip Error
6.14.E4 int((Ei(t))^(2), t = 0..infinity)= 2*ln(2) Integrate[(-ExpIntegralEi[-(t)])^(2), {t, 0, Infinity}]= 2*Log[2] Failure Successful Skip -
6.14.E5 int(cos(t)*Ci(t), t = 0..infinity)= int(sin(t)*Ssi(t), t = 0..infinity) Integrate[Cos[t]*CosIntegral[t], {t, 0, Infinity}]= Integrate[Sin[t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}] Failure Failure Skip
Fail
Complex[-2.199611725770543, -1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[Sin[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.199611725770543, 1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[Sin[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.6288153989756469, 1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[Sin[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.6288153989756469, -1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[Sin[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.14.E5 int(sin(t)*Ssi(t), t = 0..infinity)= -(1)/(4)*Pi Integrate[Sin[t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}]= -Divide[1,4]*Pi Successful Failure -
Fail
Complex[2.199611725770543, 1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[Sin[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[2.199611725770543, -1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[Sin[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.6288153989756469, -1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[Sin[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.6288153989756469, 1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[Sin[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.14.E6 int((Ci(t))^(2), t = 0..infinity)= int((Ssi(t))^(2), t = 0..infinity) Integrate[(CosIntegral[t])^(2), {t, 0, Infinity}]= Integrate[(SinIntegral[t] - Pi/2)^(2), {t, 0, Infinity}] Failure Successful Skip -
6.14.E6 int((Ssi(t))^(2), t = 0..infinity)=(1)/(2)*Pi Integrate[(SinIntegral[t] - Pi/2)^(2), {t, 0, Infinity}]=Divide[1,2]*Pi Failure Successful Skip -
6.14.E7 int(Ci(t)*Ssi(t), t = 0..infinity)= ln(2) Integrate[CosIntegral[t]*SinIntegral[t] - Pi/2, {t, 0, Infinity}]= Log[2] Failure Failure Skip
Fail
Complex[0.7210663818131499, 1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[CosIntegral[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.7210663818131499, -1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[CosIntegral[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.1073607429330403, -1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[CosIntegral[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.1073607429330403, 1.4142135623730951] <- {Rule[Integrate[Plus[Times[Rational[-1, 2], Pi], Times[CosIntegral[t], SinIntegral[t]]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.15.E1 sum(Ci(Pi*n), n = 1..infinity)=(1)/(2)*(ln(2)- gamma) Sum[CosIntegral[Pi*n], {n, 1, Infinity}]=Divide[1,2]*(Log[2]- EulerGamma) Failure Failure Skip
Fail
Complex[1.356247804543889, 1.4142135623730951] <- {Rule[Sum[CosIntegral[Times[n, Pi]], {n, 1, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.356247804543889, -1.4142135623730951] <- {Rule[Sum[CosIntegral[Times[n, Pi]], {n, 1, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4721793202023012, -1.4142135623730951] <- {Rule[Sum[CosIntegral[Times[n, Pi]], {n, 1, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4721793202023012, 1.4142135623730951] <- {Rule[Sum[CosIntegral[Times[n, Pi]], {n, 1, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.15.E2 sum((Ssi(Pi*n))/(n), n = 1..infinity)=(1)/(2)*Pi*(ln(Pi)- 1) Sum[Divide[SinIntegral[Pi*n] - Pi/2,n], {n, 1, Infinity}]=Divide[1,2]*Pi*(Log[Pi]- 1) Failure Failure Skip
Fail
Complex[1.1868723893034128, 1.4142135623730951] <- {Rule[Sum[Times[Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[n, Pi]]]], {n, 1, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.1868723893034128, -1.4142135623730951] <- {Rule[Sum[Times[Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[n, Pi]]]], {n, 1, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6415547354427775, -1.4142135623730951] <- {Rule[Sum[Times[Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[n, Pi]]]], {n, 1, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6415547354427775, 1.4142135623730951] <- {Rule[Sum[Times[Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[n, Pi]]]], {n, 1, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.15.E3 sum((- 1)^(n)* Ci(2*Pi*n), n = 1..infinity)= 1 - ln(2)-(1)/(2)*gamma Sum[(- 1)^(n)* CosIntegral[2*Pi*n], {n, 1, Infinity}]= 1 - Log[2]-Divide[1,2]*EulerGamma Failure Failure Skip
Fail
Complex[1.395968575383807, 1.4142135623730951] <- {Rule[Sum[Times[Power[-1, n], CosIntegral[Times[2, n, Pi]]], {n, 1, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.395968575383807, -1.4142135623730951] <- {Rule[Sum[Times[Power[-1, n], CosIntegral[Times[2, n, Pi]]], {n, 1, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4324585493623831, -1.4142135623730951] <- {Rule[Sum[Times[Power[-1, n], CosIntegral[Times[2, n, Pi]]], {n, 1, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4324585493623831, 1.4142135623730951] <- {Rule[Sum[Times[Power[-1, n], CosIntegral[Times[2, n, Pi]]], {n, 1, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.15.E4 sum((- 1)^(n)*(Ssi(2*Pi*n))/(n), n = 1..infinity)= Pi*((3)/(2)*ln(2)- 1) Sum[(- 1)^(n)*Divide[SinIntegral[2*Pi*n] - Pi/2,n], {n, 1, Infinity}]= Pi*(Divide[3,2]*Log[2]- 1) Failure Failure Skip Error
6.16.E1 sin(x)+(1)/(3)*sin(3*x)+(1)/(5)*sin(5*x)+ .. = Sin[x]+Divide[1,3]*Sin[3*x]+Divide[1,5]*Sin[5*x]+ ... = Error Failure - -
6.16.E1 Error Failure - Error
6.16.E1 x < Pi , 0 , x < Pi , 0 , Error Failure - Error
6.18#Ex1 A[n]= int((t*exp(- z*t))/(1 + (t)^(2))*(((t)^(2))/(1 + (t)^(2)))^(n), t = 0..infinity) Subscript[A, n]= Integrate[Divide[t*Exp[- z*t],1 + (t)^(2)]*(Divide[(t)^(2),1 + (t)^(2)])^(n), {t, 0, Infinity}] Failure Failure Skip Error
6.18#Ex2 B[n]= int((exp(- z*t))/(1 + (t)^(2))*(((t)^(2))/(1 + (t)^(2)))^(n), t = 0..infinity) Subscript[B, n]= Integrate[Divide[Exp[- z*t],1 + (t)^(2)]*(Divide[(t)^(2),1 + (t)^(2)])^(n), {t, 0, Infinity}] Failure Failure Skip Error
6.18#Ex3 C[n]= int(exp(- z*t)*(((t)^(2))/(1 + (t)^(2)))^(n), t = 0..infinity) Subscript[C, n]= Integrate[Exp[- z*t]*(Divide[(t)^(2),1 + (t)^(2)])^(n), {t, 0, Infinity}] Failure Failure Skip Error