Formula:KLS:09.15:18

<< Formula:KLS:09.15:17

formula in Hermite

Formula:KLS:09.15:19 >>

${\displaystyle{\displaystyle{\displaystyle\frac{1+2xt+4t^{2}}{(1+4t^{2})^{\frac{3}{2}}}\exp\left(\frac{4x^{2}t^{2}}{1+4t^{2}}\right)=\sum_{n=0}^{\infty}\frac{H_{n}\left(x\right)}{\lfloor n/2\rfloor\,!}t^{n}}}}$

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
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : Hermite polynomial ${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : http://dlmf.nist.gov/18.3#T1.t1.r28

Bibliography

Equation in Section 9.15 of KLS.

URL links

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<< Formula:KLS:09.15:17

formula in Hermite

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