Ey let me change the title god damn it

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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 ln ⁡ 1 = 0 1 0 {\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 ln ⁡ 1 = 0 1 0 {\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 ( n k ) = n ! ( n - k ) ! ⁢ k ! binomial 𝑛 𝑘 𝑛 𝑛 𝑘 𝑘 {\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 ( λ - i ⁢ τ a , b ⁢ ( θ ) ) n n ! ⁢ e i ⁢ n ⁢ θ ⁢ F 1 2 ⁡ ( - n , λ + i ⁢ τ a , b ⁢ ( θ ) - n - λ + 1 + i ⁢ τ a , b ⁢ ( θ ) ; e - 2 ⁢ i ⁢ θ ) = ∑ ℓ = 0 n ( λ + i ⁢ τ a , b ⁢ ( θ ) ) ℓ ℓ ! ⁢ ( λ - i ⁢ τ a , b ⁢ ( θ ) ) n - ℓ ( n - ℓ ) ! ⁢ e i ⁢ ( n - 2 ⁢ ℓ ) ⁢ θ Pochhammer 𝜆 imaginary-unit subscript 𝜏 𝑎 𝑏 𝜃 𝑛 𝑛 superscript 𝑒 imaginary-unit 𝑛 𝜃 Gauss-hypergeometric-F-as-2F1 𝑛 𝜆 imaginary-unit subscript 𝜏 𝑎 𝑏 𝜃 𝑛 𝜆 1 imaginary-unit subscript 𝜏 𝑎 𝑏 𝜃 superscript 𝑒 2 imaginary-unit 𝜃 superscript subscript ℓ 0 𝑛 Pochhammer 𝜆 imaginary-unit subscript 𝜏 𝑎 𝑏 𝜃 ℓ ℓ Pochhammer 𝜆 imaginary-unit subscript 𝜏 𝑎 𝑏 𝜃 𝑛 ℓ 𝑛 ℓ superscript 𝑒 imaginary-unit 𝑛 2 ℓ 𝜃 {\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}		 0 < θ , θ < π formulae-sequence 0 𝜃 𝜃 𝜋 {\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 n ! ( n - k ) ! ⁢ k ! = ( n n - k ) 𝑛 𝑛 𝑘 𝑘 binomial 𝑛 𝑛 𝑘 {\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 ( - 1 ) k ⁢ ( - z ) k k ! = ( - 1 ) k ⁢ ( k - z - 1 k ) superscript 1 𝑘 Pochhammer 𝑧 𝑘 𝑘 superscript 1 𝑘 binomial 𝑘 𝑧 1 𝑘 {\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 ( z + 1 k ) = ( z k ) + ( z k - 1 ) binomial 𝑧 1 𝑘 binomial 𝑧 𝑘 binomial 𝑧 𝑘 1 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{z+1}{k}=\genfrac{(}{)}{0.0% pt}{}{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 ∑ k = 0 m ( z + k k ) = ( z + m + 1 m ) subscript superscript 𝑚 𝑘 0 binomial 𝑧 𝑘 𝑘 binomial 𝑧 𝑚 1 𝑚 {\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 n ⁢ a + 1 2 ⁢ n ⁢ ( n - 1 ) ⁢ d = 1 2 ⁢ n ⁢ ( a + ℓ ) 𝑛 𝑎 1 2 𝑛 𝑛 1 𝑑 1 2 𝑛 𝑎 ℓ {\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 M ⁢ ( r ) = 0 𝑀 𝑟 0 {\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 M ⁢ ( 1 ) = A 𝑀 1 𝐴 {\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 M ⁢ ( - 1 ) = H 𝑀 1 𝐻 {\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 lim r → 0 ⁡ M ⁢ ( r ) = G subscript → 𝑟 0 𝑀 𝑟 𝐺 {\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 - -
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