test

Notation

1.1 Special Notation

Areas

1.2 Elementary Algebra
1.3 Determinants
1.4 Calculus of One Variable
1.5 Calculus of Two or More Variables
1.6 Vectors and Vector-Valued Functions
1.7 Inequalities
1.8 Fourier Series
1.9 Calculus of a Complex Variable
1.10 Functions of a Complex Variable
1.11 Zeros of Polynomials
1.12 Continued Fractions
1.13 Differential Equations
1.14 Integral Transforms
1.15 Summability Methods
1.16 Distributions
1.17 Integral and Series Representations of the Dirac Delta

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
4.4.E1	${\displaystyle{\displaystyle\ln 1=0}}$ - Mit Item:QID \ln@@{1} = 0		ln(1) = 0	Log[1] == 0	Successful	Successful	-	Successful [Tested: 1]
4.4.E1	${\displaystyle{\displaystyle\ln 1=0}}$ - Mit Math-QID \ln@@{1} = 0		ln(1) = 0	Log[1] == 0	Successful	Successful	-	Successful [Tested: 1]
1.2.E1	${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}=\frac{n!}{(n-k)!k!}}}$ \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	-	Successful [Tested: 9]
18.35.E4	${\displaystyle{\displaystyle\frac{{\left(\lambda-\mathrm{i}\tau_{a,b}(\theta)\right)_{n}}}{n!}e^{\mathrm{i}n\theta}\*{{}_{2}F_{1}}\left({-n,\lambda+\mathrm{i}\tau_{a,b}(\theta)\atop-n-\lambda+1+\mathrm{i}\tau_{a,b}(\theta)};e^{-2\mathrm{i}\theta}\right)=\sum_{\ell=0}^{n}\frac{{\left(\lambda+\mathrm{i}\tau_{a,b}(\theta)\right)_{\ell}}}{\ell!}\frac{{\left(\lambda-\mathrm{i}\tau_{a,b}(\theta)\right)_{n-\ell}}}{(n-\ell)!}e^{\mathrm{i}(n-2\ell)\theta}}}$ \frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n}}{n!}e^{\iunit n\theta}\*\genhyperF{2}{1}@@{-n,\lambda+\iunit\tau_{a,b}(\theta)}{-n-\lambda+1+\iunit\tau_{a,b}(\theta)}{e^{-2\iunit\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda+\iunit\tau_{a,b}(\theta)}{\ell}}{\ell!}\frac{\Pochhammersym{\lambda-\iunit\tau_{a,b}(\theta)}{n-\ell}}{(n-\ell)!}e^{\iunit(n-2\ell)\theta}	${\displaystyle{\displaystyle 0<\theta,\theta<\pi}}$	(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n))/(factorial(n))*exp(I*n*theta)* hypergeom([- n , lambda + I*((a*cos(theta)+ b)/(sin(theta)))], [- n - lambda + 1 + I*((a*cos(theta)+ b)/(sin(theta)))], exp(- 2*I*theta)) = sum((pochhammer(lambda + I*((a*cos(theta)+ b)/(sin(theta))), ell))/(factorial(ell))*(pochhammer(lambda - I*((a*cos(theta)+ b)/(sin(theta))), n - ell))/(factorial(n - ell))*exp(I*(n - 2*ell)*theta), ell = 0..n)	Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n],(n)!]*Exp[I*n*\[Theta]]* HypergeometricPFQ[{- n , \[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, {- n - \[Lambda]+ 1 + I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]])}, Exp[- 2*I*\[Theta]]] == Sum[Divide[Pochhammer[\[Lambda]+ I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), \[ScriptL]],(\[ScriptL])!]*Divide[Pochhammer[\[Lambda]- I*(Divide[a*Cos[\[Theta]]+ b,Sin[\[Theta]]]), n - \[ScriptL]],(n - \[ScriptL])!]*Exp[I*(n - 2*\[ScriptL])*\[Theta]], {\[ScriptL], 0, n}, GenerateConditions->None]	Error	Successful	-	Successful [Tested: 300]
1.2.E1	${\displaystyle{\displaystyle\frac{n!}{(n-k)!k!}=\genfrac{(}{)}{0.0pt}{}{n}{n-k}}}$ \frac{n!}{(n-k)!k!} = \binom{n}{n-k}		(factorial(n))/(factorial(n - k)*factorial(k)) = binomial(n,n - k)	Divide[(n)!,(n - k)!*(k)!] == Binomial[n,n - k]	Successful	Successful	-	Successful [Tested: 9]
1.2.E6	${\displaystyle{\displaystyle\frac{(-1)^{k}{\left(-z\right)_{k}}}{k!}=(-1)^{k}\genfrac{(}{)}{0.0pt}{}{k-z-1}{k}}}$ \frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}		((- 1)^(k)* pochhammer(- z, k))/(factorial(k)) = (- 1)^(k)*binomial(k - z - 1,k)	Divide[(- 1)^(k)* Pochhammer[- z, k],(k)!] == (- 1)^(k)*Binomial[k - z - 1,k]	Successful	Successful	-	Successful [Tested: 21]
1.2.E7	${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{z+1}{k}=\genfrac{(}{)}{0.0pt}{}{z}{k}+\genfrac{(}{)}{0.0pt}{}{z}{k-1}}}$ \binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}		binomial(z + 1,k) = binomial(z,k)+binomial(z,k - 1)	Binomial[z + 1,k] == Binomial[z,k]+Binomial[z,k - 1]	Successful	Successful	-	Successful [Tested: 21]
1.2.E8	${\displaystyle{\displaystyle\sum^{m}_{k=0}\genfrac{(}{)}{0.0pt}{}{z+k}{k}=\genfrac{(}{)}{0.0pt}{}{z+m+1}{m}}}$ \sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}		sum(binomial(z + k,k), k = 0..m) = binomial(z + m + 1,m)	Sum[Binomial[z + k,k], {k, 0, m}, GenerateConditions->None] == Binomial[z + m + 1,m]	Successful	Successful	-	Successful [Tested: 21]
1.2.E10	${\displaystyle{\displaystyle na+\tfrac{1}{2}n(n-1)d=\tfrac{1}{2}n(a+\ell)}}$ na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)		n*a +(1)/(2)*n*(n - 1)*d = (1)/(2)*n*(a + ell)	n*a +Divide[1,2]*n*(n - 1)*d == Divide[1,2]*n*(a + \[ScriptL])	Skipped - no semantic math	Skipped - no semantic math	-	-
1.2.E22	${\displaystyle{\displaystyle M(r)=0}}$ M(r) = 0		((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r)) = 0	((Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r)) == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
1.2#Ex1	${\displaystyle{\displaystyle M(1)=A}}$ M(1) = A		M(1) = ((a[1]+ a[2]+ .. + a[n])/(n))	M[1] == (Divide[Subscript[a, 1]+ Subscript[a, 2]+ \[Ellipsis]+ Subscript[a, n],n])	Skipped - no semantic math	Skipped - no semantic math	-	-
1.2#Ex2	${\displaystyle{\displaystyle M(-1)=H}}$ M(-1) = H		M(- 1) = H	M[- 1] == H	Skipped - no semantic math	Skipped - no semantic math	-	-
1.2.E26	${\displaystyle{\displaystyle\lim_{r\to 0}M(r)=G}}$ \lim_{r\to 0}M(r) = G		limit((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r), r = 0) = ((a[1]*a[2] .. a[n])^(1/n))	Limit[(Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r), r -> 0, GenerateConditions->None] == ((Subscript[a, 1]*Subscript[a, 2] \[Ellipsis]Subscript[a, n])^(1/n))	Skipped - no semantic math	Skipped - no semantic math	-	-