Formula:KLS:09.13:12

<< Formula:KLS:09.13:11

formula in Bessel

Formula:KLS:09.13:13 >>

${\displaystyle{\displaystyle{\displaystyle\left(1-2xt\right)^{-\frac{1}{2}}\left(\frac{2}{1+\sqrt{1-2xt}}\right)^{a}\exp\left(\frac{2t}{1+\sqrt{1-2xt}}\right)=\sum_{n=0}^{\infty}y_{n}\!\left(x;a\right)\frac{t^{n}}{n!}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{exp}}}}$ : exponential function : http://dlmf.nist.gov/4.2#E19
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle y_{n}}}}$ : Bessel polynomial : http://dlmf.nist.gov/18.34#E1

Bibliography

Equation in Section 9.13 of KLS.

URL links

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formula in Bessel

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