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\sum_{x=0}^{\infty}\frac{\pochhammer{\beta}{x}}{x!}c^x\Meixner{m}@{x}{\beta}{c}\Meixn <div align="right">Constraint(s): <math>{\displaystyle \beta > 0\quad 0 < c < 1}</math></div><br /> ...

...n+\alpha+1-x)\Laguerre[\alpha]{n}@{x}+(n+\alpha)\Laguerre[\alpha]{n-1}@{x}=0 xy''(x)+(\alpha+1-x)y'(x)+ny(x)=0 ...

<div align="right">Constraint(s): <math>{\displaystyle c<0}</math></div><br /> \qHyperrphis{2}{1}@@{qx^{-1},0}{q}{q}{xt}\,\qHyperrphis{1}{1}@@{c^{-1}x}{q}{q}{cqt} ...

...de>Sum[Divide[Pochhammer[a, k],Pochhammer[b, k]]*Divide[(z)^(k),(k)!], {k, 0, m}]=Divide[Pochhammer[a, m]*(z)^(m),Pochhammer[b, m]*(m)!]*HypergeometricP ...[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 4.0] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}< ...

...n}@{x}{q}=\frac{1}{\qPochhammer{q}{q}{n}}\,\qHyperrphis{2}{1}@@{q^{-n},-x}{0}{q}{q^{n+\alpha+1}} \int_{0}^{\infty}\frac{x^{\alpha}}{\qPochhammer{-x}{q}{\infty}}\qLaguerre[\alpha]{m ...

...n}@{x}{q}=\frac{1}{\qPochhammer{q}{q}{n}}\,\qHyperrphis{2}{1}@@{q^{-n},-x}{0}{q}{q^{n+\alpha+1}} \int_{0}^{\infty}\frac{x^{\alpha}}{\qPochhammer{-x}{q}{\infty}}\qLaguerre[\alpha]{m ...

...s{3}{2}@@{q^{-n},a\expe^{\iunit(\theta+2\phi)},a\expe^{-\iunit\theta}}{a^2,0}{q}{q} <div align="right">Constraint(s): <math>{\displaystyle 0<a<1}</math></div><br /> ...

...s{3}{2}@@{q^{-n},a\expe^{\iunit(\theta+2\phi)},a\expe^{-\iunit\theta}}{a^2,0}{q}{q} <div align="right">Constraint(s): <math>{\displaystyle 0<a<1}</math></div><br /> ...

\Charlier{n}@{x}{a}=\HyperpFq{2}{0}@@{-n,-x}{-}{-\frac{1}{a}} \sum_{x=0}^{\infty}\frac{a^x}{x!}\Charlier{m}@{x}{a}\Charlier{n}@{x}{a}= ...

...|| <code>(Subscript[S, m*n])^(1)*(\[Gamma], 0)=(- 1)^(m)* LegendreP[n, m, 0]</code> || Failure || Failure || Error || Error ..., Power[2, Rational[1, 2]]]]}</code><br><code>Complex[33.660899653979236, -0.8858131487889274] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]] ...

{}+n(n+\alpha+\beta+1)y(x)=0 \sum_{n=0}^{\infty}\Jacobi{\alpha}{\beta}{n}@{x}t^n ...

<div align="right">Constraint(s): <math>{\displaystyle \lambda > 0\quad 0 < \phi < \cpi}</math></div><br /> {}+(n+2\lambda-1)\MeixnerPollaczek{\lambda}{n-1}@{x}{\phi}=0 ...

<div align="right">Constraint(s): <math>{\displaystyle n=0,1,2,\ldots,N}</math></div><br /> \qPochhammer{q^{-x},\gamma\delta q^{x+1}}{q}{k}=\prod_{j=0}^{k-1}\left(1-\mu(x)q^j+\gamma\delta q^{2j+1}\right) ...

<div align="right">Constraint(s): <math>{\displaystyle n=0,1,2,\ldots,N}</math></div><br /> \qPochhammer{q^{-x},\gamma\delta q^{x+1}}{q}{k}=\prod_{j=0}^{k-1}\left(1-\mu(x)q^j+\gamma\delta q^{2j+1}\right) ...

...D[w, {z, 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[z, (k)^2])^(2))* w = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-co ...^(- 2)- \[Nu]*(\[Nu]+ 1)* \[Xi],4*\[Xi]*(\[Xi]- 1)*(\[Xi]- (k)^(- 2))]*w = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-co ...

\sum_{n=0}^\infty\frac{\pochhammer{\alpha+\beta+1}{n} n!}{\pochhammer{\alpha+1}{n}\po \sum_{n=0}^\infty\frac{2n+\alpha+\beta+1}{n+\alpha+\beta+1} ...

\sum_{k=0}^{\infty}\frac{\qPochhammer{bq}{q}{k}}{\qPochhammer{q}{q}{k}}(aq)^k\littleq ...0}{1}@@{-}{aq}{q}{aqxt}\,\qHyperrphis{2}{1}@@{x^{-1},0}{bq}{q}{xt}=\sum_{n=0}^{\infty} ...

...mes[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 3.141592653589793] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, ...egralEi[-(z)] + Ln[z] + EulerGamma = Integrate[Divide[1 - Exp[- t],t], {t, 0, z}]</code> || Error || Failure || - || Successful ...

\discrqHermiteII{n}@{x}{q}=\iunit^{-n}q^{-\binomial{n}{2}}\,\qHyperrphis{2}{0}@@{q^{-n},\iunit x}{-}{q}{-q^n} \qHyperrphis{2}{1}@@{q^{-n},q^{-n+1}}{0}{q^2}{-\frac{q^2}{x^2}} ...

<div align="right">Constraint(s): <math>{\displaystyle n=0,1,2,\ldots,N}</math></div><br /> (1+x^2)y''(x)+2\left(\nu-Nx\right)y'(x)-n(n-2N-1)y(x)=0 ...