Gold 64

Meixner polynomials

Gold ID

64

Link

https://sigir21.wmflabs.org/wiki/Meixner_polynomials#math.116.0

Formula

$M_n(x,\beta ,\gamma )=\sum _{k=0}^n(-1{)}^k(\genfrac{}{}{0ex}{}{n}{k})(\genfrac{}{}{0ex}{}{x}{k})k!(x+\beta {)}_{n-k}{\gamma }^{-k}$

TeX Source

M_n(x,\beta,\gamma) = \sum_{k=0}^n (-1)^k{n \choose k}{x\choose k}k!(x+\beta)_{n-k}\gamma^{-k}

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

M_n(x , \beta , \gamma) = \sum_{k=0}^n(- 1)^k{n \choose k}{x\choose k} k! \Pochhammersym{x + \beta}{n-k} \gamma^{-k}

Expected (Gold Entry)

\MeixnerpolyM{n}@{x}{\beta}{\gamma} = \sum_{k=0}^n(- 1)^k{n \choose k}{x\choose k} k! \Pochhammersym{x + \beta}{n-k} \gamma^{-k}

Mathematica

Translation

Subscript[\[CapitalMu], n][x , \[Beta], \[Gamma]] == Sum[(- 1)^(k)*Binomial[n,k]*Binomial[x,k]*(k)!*Pochhammer[x + \[Beta], n - k]*\[Gamma]^(- k), {k, 0, n}, GenerateConditions->None]

Expected (Gold Entry)

M[n_, x_, \[Beta]_, \[Gamma]_] := Sum[(- 1)^(k)*Binomial[n,k]*Binomial[x,k]*(k)!*Pochhammer[x + \[Beta], n - k]*\[Gamma]^(- k), {k, 0, n}]

Maple

Translation

Mu[n](x , beta , gamma) = sum((- 1)^(k)*binomial(n,k)*binomial(x,k)*factorial(k)*pochhammer(x + beta, n - k)*(gamma)^(- k), k = 0..n)

Expected (Gold Entry)