Formula:KLS:14.22:19

<< Formula:KLS:14.22:18

formula in q-Bessel

Formula:KLS:14.22:20 >>

${\displaystyle{\displaystyle{\displaystyle\qHyperrphis{0}{1}@@{-}{0}{q}{-aq^{x+1}t}\,\qHyperrphis{2}{0}@@{q^{-x},0}{-}{q}{q^{x}t}{}=\sum_{n=0}^{\infty}\frac{y_{n}\!\left(q^{x};a;q\right)}{\left(q;q\right)_{n}}t^{n}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle x=0,1,2,\ldots}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle y_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Bessel polynomial : http://drmf.wmflabs.org/wiki/Definition:qBessel
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.22 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.22:18

formula in q-Bessel

Formula:KLS:14.22:20 >>