Formula:KLS:01.04:10

<< Formula:KLS:01.04:09

formula in Hypergeometric functions

Formula:KLS:01.04:11 >>

${\displaystyle{\displaystyle{\displaystyle{\mathrm{e}^{t}}\,\HyperpFq{1}{1}@@{-x}{-N}{-\frac{t}{p}}=\sum_{k=0}^{\infty}\frac{t^{k}}{k!}\sum_{m=0}^{x}\frac{{\left(-x\right)_{m}}}{{\left(-N\right)_{m}}m!}\left(-\frac{t}{p}\right)^{m}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 1.4 of KLS.

URL links

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formula in Hypergeometric functions

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