Search results

\qBesselPoly{n}@{x}{a}{q}=\qHyperrphis{2}{1}@@{q^{-n},-aq^n}{0}{q}{qx} ...n}@{x}{a}{q}=\left(-aq^nx\right)^n\cdot\qHyperrphis{2}{1}@@{q^{-n},x^{-1}}{0}{q}{-\frac{q^{-n+1}}{a}} ...

<div align="right">Constraint(s): <math>{\displaystyle n=0,1,2,\ldots,N}</math></div><br /> \sum_{x=0}^N\binomial{N}{x}p^x(1-p)^{N-x} \Krawtchouk{m}@{x}{p}{N}\Krawtchouk{n}@{x}{ ...

\littleqLaguerre{n}@{x}{a}{q}=\qHyperrphis{2}{1}@@{q^{-n},0}{aq}{q}{qx} ...e{n}@{x}{a}{q}=\frac{1}{\qPochhammer{a^{-1}q^{-n}}{q}{n}}\,\qHyperrphis{2}{0}@@{q^{-n},x^{-1}}{-}{q}{\frac{x}{a}} ...

...}{n} = 0</math>]] || <code>binomial(m,n)= 0</code> || <code>Binomial[m,n]= 0</code> || Failure || Failure || Skip || Successful ...^(n), n = 0..m)=(1 + x)^(m)</code> || <code>Sum[Binomial[m,n]*(x)^(n), {n, 0, m}]=(1 + x)^(m)</code> || Successful || Successful || - || - ...

<div align="right">Constraint(s): <math>{\displaystyle \realpart{z}>0}</math></div><br /> <div align="right">Constraint(s): <math>{\displaystyle \alpha\neq 0}</math></div><br /> ...

<div align="right">Constraint(s): <math>{\displaystyle n=0,1,2,\ldots,N}</math></div><br /> \sum_{x=0}^N\binomial{\alpha +x}{x}\binomial{\beta+N-x}{N-x}\Hahn{m}@{x}{\alpha}{\bet ...

\RiemannZeta@{s} = \frac{1}{1 - 2^{-s}} \sum_{n=0}^\infty \frac{1}{(2n+1)^s} <div align="right">Constraint(s): <math>{\displaystyle \realpart{s} > 0}</math></div><br /> ...

<div align="right">Constraint(s): <math>{\displaystyle 0<q<1}</math></div><br /> <div align="right">Constraint(s): <math>{\displaystyle k=0,1,2,\ldots,n}</math></div><br /> ...

...houk{n}@{q^{-x}}{p}{N}{q}=\qHyperrphis{3}{2}@@{q^{-n},q^{-x},-pq^n}{q^{-N},0}{q}{q} \sum_{x=0}^N\frac{\qPochhammer{q^{-N}}{q}{x}}{\qPochhammer{q}{q}{x}}(-p)^{-x}\qKrawtc ...

...houk{n}@{q^{-x}}{p}{N}{q}=\qHyperrphis{3}{2}@@{q^{-n},q^{-x},-pq^n}{q^{-N},0}{q}{q} \sum_{x=0}^N\frac{\qPochhammer{q^{-N}}{q}{x}}{\qPochhammer{q}{q}{x}}(-p)^{-x}\qKrawtc ...

\ctsqHermite{n}@{x}{q}=\expe^{\iunit n\theta}\,\qHyperrphis{2}{0}@@{q^{-n},0}{-}{q}{q^n\expe^{-2\iunit\theta}} <math>{\displaystyle h(x,\alpha):=\prod_{k=0}^{\infty}\left(1-2\alpha xq^k+\alpha^2q^{2k}\right) ...

\AffqKrawtchouk{n}@{q^{-x}}{p}{N}{q}=\qHyperrphis{3}{2}@@{q^{-n},0,q^{-x}}{pq,q^{-N}}{q}{q} <div align="right">Constraint(s): <math>{\displaystyle n=0,1,2,\ldots,N}</math></div><br /> ...

\qCharlier{n}@{q^{-x}}{a}{q}=\qHyperrphis{2}{1}@@{q^{-n},q^{-x}}{0}{q}{-\frac{q^{n+1}}{a}} \sum_{x=0}^{\infty}\frac{a^x}{\qPochhammer{q}{q}{x}}q^{\binomial{x}{2}}\qCharlier{m}@ ...

\qCharlier{n}@{q^{-x}}{a}{q}=\qHyperrphis{2}{1}@@{q^{-n},q^{-x}}{0}{q}{-\frac{q^{n+1}}{a}} \sum_{x=0}^{\infty}\frac{a^x}{\qPochhammer{q}{q}{x}}q^{\binomial{x}{2}}\qCharlier{m}@ ...

...e>EllipticTheta[1, 0, q]= (D[EllipticTheta[2, temp, q], {temp, 1}]/.temp-> 0)</code> || Successful || Successful || - || - ...], {temp, 1}]/.temp-> 0)= (D[EllipticTheta[3, temp, q], {temp, 1}]/.temp-> 0)</code> || Failure || Successful || Error || - ...

\Hermite{n}@{x}=(2x)^n\,\HyperpFq{2}{0}@@{-n/2,-(n-1)/2}{-}{-\frac{1}{x^2}} \Hermite{n+1}@{x}-2x\Hermite{n}@{x}+2n\Hermite{n-1}@{x}=0 ...

...qHyperrphis{3}{2}@@{q^{-n},a\expe^{\iunit\theta},a\expe^{-\iunit\theta}}{0,0}{q}{q} \ctsbigqHermite{n}@{x}{a}{q}=\expe^{\iunit n\theta}\,\qHyperrphis{2}{0}@@{q^{-n},a\expe^{\iunit\theta}}{-}{q}{q^n\expe^{-2\iunit\theta}} ...

\bigqLaguerre{n}@{x}{a}{b}{q}=\qHyperrphis{3}{2}@@{q^{-n},0,x}{aq,bq}{q}{q} \qPochhammer{bqt}{q}{\infty}\cdot\qHyperrphis{2}{1}@@{aqx^{-1},0}{aq}{q}{xt} ...

<div align="right">Constraint(s): <math>{\displaystyle n=0,1,2,\ldots,N}</math></div><br /> \sum_{x=0}^N\frac{\qPochhammer{\alpha q,q^{-N}}{q}{x}}{\qPochhammer{q,\beta^{-1}q^{-N ...

<div align="right">Constraint(s): <math>{\displaystyle n=0,1,2,\ldots,N}</math></div><br /> \sum_{x=0}^N\frac{\qPochhammer{\alpha q,q^{-N}}{q}{x}}{\qPochhammer{q,\beta^{-1}q^{-N ...