DLMF Results: Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
No edit summary
No edit summary
Line 4: Line 4:
|-
|-
| [[Item:Q30|1.2.E1]] || <math>\binom{n}{k} = \frac{n!}{(n-k)!k!}</math> || <code>binomial(n,k)=(factorial(n))/(factorial(n - k)*factorial(k))</code> || <code>Binomial[n,k]=Divide[(n)!,(n - k)!*(k)!]</code> || Successful || Successful || - || -  
| [[Item:Q30|1.2.E1]] || <math>\binom{n}{k} = \frac{n!}{(n-k)!k!}</math> || <code>binomial(n,k)=(factorial(n))/(factorial(n - k)*factorial(k))</code> || <code>Binomial[n,k]=Divide[(n)!,(n - k)!*(k)!]</code> || Successful || Successful || - || -  
|-
| [[Item:Q30|1.2.E1]] || <math>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</math> || <code>(factorial(n))/(factorial(n - k)*factorial(k))=binomial(n,n - k)</code> || <code>Divide[(n)!,(n - k)!*(k)!]=Binomial[n,n - k]</code> || Successful || Successful || - || -
|-
| [[Item:Q35|1.2.E6]] || <math>\binom{z}{k} = \frac{z(z-1)\cdots(z-k+1)}{k!}</math> || <code>binomial(z,k)=(z*(z - 1)..(z - k + 1))/(factorial(k))</code> || <code>Binomial[z,k]=Divide[z*(z - 1) ... (z - k + 1),(k)!]</code> || Successful || Successful || - || -
|-
| [[Item:Q36|1.2.E7]] || <math>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</math> || <code>binomial(z + 1,k)=binomial(z,k)+binomial(z,k - 1)</code> || <code>Binomial[z + 1,k]=Binomial[z,k]+Binomial[z,k - 1]</code> || Successful || Successful || - || -
|-
| [[Item:Q37|1.2.E8]] || <math>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</math> || <code>sum(binomial(z + k,k), k = 0..m)=binomial(z + m + 1,m)</code> || <code>Sum[Binomial[z + k,k], {k, 0, m}]=Binomial[z + m + 1,m]</code> || Successful || Successful || - || -
|-
| [[Item:Q87|1.4.E8]] || <math>f^{(2)}(x) = \deriv[2]{f}{x}</math> || <code>(f)^(2)*(x)= diff(f, [x$(2)])</code> || <code>(f)^(2)*(x)= D[f, {x, 2}]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.+3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>0.+7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>0.+11.99999999*I <- {f = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>0.-3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), x = 1}</code><br><code>0.-7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), x = 2}</code><br><code>0.-11.99999999*I <- {f = 2^(1/2)-I*2^(1/2), x = 3}</code><br><code>0.+3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), x = 1}</code><br><code>0.+7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), x = 2}</code><br><code>0.+11.99999999*I <- {f = -2^(1/2)-I*2^(1/2), x = 3}</code><br><code>0.-3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), x = 1}</code><br><code>0.-7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), x = 2}</code><br><code>0.-11.99999999*I <- {f = -2^(1/2)+I*2^(1/2), x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, 12.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, -12.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, 12.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}</code><br><code>Complex[0.0, -12.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}</code><br></div></div>
|-
| [[Item:Q87|1.4.E8]] || <math>\deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)</math> || <code>diff(f, [x$(2)])= diff(diff(f, x), x)</code> || <code>D[f, {x, 2}]= D[D[f, x], x]</code> || Successful || Successful || - || -
|-
| [[Item:Q88|1.4.E9]] || <math>f^{(n)} = f^{(n)}(x)</math> || <code>(f)^(n)= (f)^(n)*(x)</code> || <code>(f)^(n)= (f)^(n)*(x)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.414213562-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>-2.828427124-2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>-0.-3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-0.-7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245-5.656854245*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>11.31370849-11.31370849*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br><code>-1.414213562+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>-2.828427124+2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>-0.+3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-0.+7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245+5.656854245*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>11.31370849+11.31370849*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>1.414213562+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>2.828427124+2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>-0.-3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-0.-7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245+5.656854245*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>-11.31370849+11.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>1.414213562-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>2.828427124-2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>-0.+3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-0.+7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245-5.656854245*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>-11.31370849-11.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br></div></div>
|-
| [[Item:Q88|1.4.E9]] || <math>f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)</math> || <code>(f)^(n)*(x)= diff((f)^(n - 1)*(x), x)</code> || <code>(f)^(n)*(x)= D[(f)^(n - 1)*(x), x]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.414213562+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 1}</code><br><code>1.828427124+2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>3.242640686+4.242640686*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>-1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 1}</code><br><code>-1.414213562+6.585786434*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>-1.414213562+10.58578643*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245+1.656854247*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 1}</code><br><code>-11.31370849+7.313708492*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>-16.97056274+12.97056274*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br><code>.414213562-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 1}</code><br><code>1.828427124-2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>3.242640686-4.242640686*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>-1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 1}</code><br><code>-1.414213562-6.585786434*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>-1.414213562-10.58578643*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>-5.656854245-1.656854247*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 1}</code><br><code>-11.31370849-7.313708492*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>-16.97056274-12.97056274*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>-2.414213562-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 1}</code><br><code>-3.828427124-2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}</code><br><code>-5.242640686-4.242640686*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}</code><br><code>1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 1}</code><br><code>1.414213562+9.414213558*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}</code><br><code>1.414213562+13.41421355*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245-9.656854243*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 1}</code><br><code>11.31370849-15.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}</code><br><code>16.97056274-20.97056274*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}</code><br><code>-2.414213562+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 1}</code><br><code>-3.828427124+2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}</code><br><code>-5.242640686+4.242640686*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}</code><br><code>1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 1}</code><br><code>1.414213562-9.414213558*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}</code><br><code>1.414213562-13.41421355*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}</code><br><code>5.656854245+9.656854243*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 1}</code><br><code>11.31370849+15.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}</code><br><code>16.97056274+20.97056274*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[1.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[3.2426406871192857, 4.242640687119286] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, 2.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[-1.4142135623730951, 6.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[-1.4142135623730951, 10.585786437626904] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, 1.6568542494923806] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[-11.313708498984761, 7.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-16.970562748477143, 12.970562748477143] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[1.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[3.2426406871192857, -4.242640687119286] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[-1.4142135623730951, -2.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[-1.4142135623730951, -6.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[-1.4142135623730951, -10.585786437626904] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[-5.656854249492381, -1.6568542494923806] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[-11.313708498984761, -7.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[-16.970562748477143, -12.970562748477143] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[-3.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-5.242640687119286, -4.242640687119286] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, 5.414213562373095] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[1.4142135623730951, 9.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[1.4142135623730951, 13.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, -9.65685424949238] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[11.313708498984761, -15.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[16.970562748477143, -20.970562748477143] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br><code>Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}</code><br><code>Complex[-3.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}</code><br><code>Complex[-5.242640687119286, 4.242640687119286] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}</code><br><code>Complex[1.4142135623730951, -5.414213562373095] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}</code><br><code>Complex[1.4142135623730951, -9.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}</code><br><code>Complex[1.4142135623730951, -13.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}</code><br><code>Complex[5.656854249492381, 9.65685424949238] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}</code><br><code>Complex[11.313708498984761, 15.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}</code><br><code>Complex[16.970562748477143, 20.970562748477143] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}</code><br></div></div>
|-
| [[Item:Q95|1.4.E16]] || <math>\int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}</math> || <code>int(f*g, x)=(int(f, x))* g - int((int(f, x))* diff(g, x), x)</code> || <code>Integrate[f*g, x]=(Integrate[f, x])* g - Integrate[(Integrate[f, x])* D[g, x], x]</code> || Successful || Successful || - || -
|-
|-
|}
|}
= Results of the Digital Library of Mathematical Functions =
<div style="-moz-column-count:2; column-count:2;">
# [[Algebraic and Analytic Methods]]
# [[Asymptotic Approximations]]
# [[Numerical Methods]]
# [[Elementary Functions]]
# [[Gamma Function]]
# [[Exponential, Logarithmic, Sine, and Cosine Integrals]]
# [[Error Functions, Dawson’s and Fresnel Integrals]]
# [[Incomplete Gamma and Related Functions]]
# [[Airy and Related Functions]]
# [[Bessel Functions]]
# [[Struve and Related Functions]]
# [[Parabolic Cylinder Functions]]
# [[Confluent Hypergeometric Functions]]
# [[Legendre and Related Functions]]
# [[Hypergeometric Function]]
# [[Generalized Hypergeometric Functions and Meijer G-Function|Generalized Hypergeometric Functions and Meijer ''G''-Function]]
# [[q-Hypergeometric and Related Functions|''q''-Hypergeometric and Related Functions]]
# [[Orthogonal Polynomials]]
# [[Elliptic Integrals]]
# [[Theta Functions]]
# [[Multidimensional Theta Functions]]
# [[Jacobian Elliptic Functions]]
# [[Weierstrass Elliptic and Modular Functions]]
# [[Bernoulli and Euler Polynomials]]
# [[Zeta and Related Functions]]
# [[Combinatorial Analysis]]
# [[Functions of Number Theory]]
# [[Mathieu Functions and Hill’s Equation]]
# [[Lamé Functions]]
# [[Spheroidal Wave Functions]]
# [[Heun Functions]]
# [[Painlevé Transcendents]]
# [[Coulomb Functions]]
# [[3j,6j,9j Symbols|''3j,6j,9j'' Symbols]]
# [[Functions of Matrix Argument]]
# [[Integrals with Coalescing Saddles]]
</div>

Revision as of 12:16, 17 January 2020

DLMF Formula Maple Mathematica Symbolic
Maple		 Symbolic
Mathematica		 Numeric
Maple		 Numeric
Mathematica
1.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}} binomial(n,k)=(factorial(n))/(factorial(n - k)*factorial(k)) Binomial[n,k]=Divide[(n)!,(n - k)!*(k)!] Successful Successful - -

Results of the Digital Library of Mathematical Functions

  1. Algebraic and Analytic Methods
  2. Asymptotic Approximations
  3. Numerical Methods
  4. Elementary Functions
  5. Gamma Function
  6. Exponential, Logarithmic, Sine, and Cosine Integrals
  7. Error Functions, Dawson’s and Fresnel Integrals
  8. Incomplete Gamma and Related Functions
  9. Airy and Related Functions
  10. Bessel Functions
  11. Struve and Related Functions
  12. Parabolic Cylinder Functions
  13. Confluent Hypergeometric Functions
  14. Legendre and Related Functions
  15. Hypergeometric Function
  16. Generalized Hypergeometric Functions and Meijer G-Function
  17. q-Hypergeometric and Related Functions
  18. Orthogonal Polynomials
  19. Elliptic Integrals
  20. Theta Functions
  21. Multidimensional Theta Functions
  22. Jacobian Elliptic Functions
  23. Weierstrass Elliptic and Modular Functions
  24. Bernoulli and Euler Polynomials
  25. Zeta and Related Functions
  26. Combinatorial Analysis
  27. Functions of Number Theory
  28. Mathieu Functions and Hill’s Equation
  29. Lamé Functions
  30. Spheroidal Wave Functions
  31. Heun Functions
  32. Painlevé Transcendents
  33. Coulomb Functions
  34. 3j,6j,9j Symbols
  35. Functions of Matrix Argument
  36. Integrals with Coalescing Saddles
Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=DLMF_Results&oldid=63433"