Gold 41

Barnes G-function

Gold ID

41

Link

https://sigir21.wmflabs.org/wiki/Barnes_G-function#math.91.47

Formula

$\frac{1}{\mathrm{\Gamma }(z)}=z{e}^{\gamma z}\prod _{k=1}^{\mathrm{\infty }}\left\{(1+\frac{z}{k})e^{-z/k}\right\}$

TeX Source

\frac{1}{\Gamma(z)}= z e^{\gamma z} \prod_{k=1}^\infty \left\{ \left(1+\frac{z}{k}\right)e^{-z/k} \right\}

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations

Semantic LaTeX

Translation

\frac{1}{\EulerGamma@{z}} = z \expe^{\EulerConstant z} \prod_{k=1}^\infty \{(1 + \frac{z}{k}) \expe^{-z/k} \}

Expected (Gold Entry)

\frac{1}{\EulerGamma@{z}} = z \expe^{\EulerConstant z} \prod_{k=1}^\infty \{(1 + \frac{z}{k}) \expe^{-z/k} \}

Mathematica

Translation

Divide[1,Gamma[z]] == z*Exp[EulerGamma*z]*Product[(1 +Divide[z,k])*Exp[- z/k], {k, 1, Infinity}, GenerateConditions->None]

Expected (Gold Entry)

Divide[1,Gamma[z]] == z*Exp[EulerGamma*z]*Product[(1 +Divide[z,k])*Exp[- z/k], {k, 1, Infinity}]

Maple

Translation

(1)/(GAMMA(z)) = z*exp(gamma*z)*product((1 +(z)/(k))*exp(- z/k), k = 1..infinity)

Expected (Gold Entry)

(1)/(GAMMA(z)) = z*exp(gamma*z)*product((1 +(z)/(k))*exp(- z/k), k = 1..infinity)