Formula:KLS:01.04:15

<< Formula:KLS:01.04:14

formula in Hypergeometric functions

Formula:KLS:01.05:01 >>

${\displaystyle{\displaystyle{\displaystyle{}J_{\nu}\left(z\right):=\frac{\left(\frac{1}{2}z\right)^{\nu}}{\Gamma\left(\nu+1\right)}\ \HyperpFq{0}{1}@@{-}{\nu+1}{-\frac{z^{2}}{4}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle J_{\nu}}}}$ : Bessel function of the first kind : http://dlmf.nist.gov/10.2#E2
${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1

Bibliography

Equation in Section 1.4 of KLS.

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formula in Hypergeometric functions

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