Formula:KLS:09.15:15

<< Formula:KLS:09.15:14

formula in Hermite

Formula:KLS:09.15:16 >>

${\displaystyle{\displaystyle{\displaystyle{\mathrm{e}^{-t^{2}}}\sinh\left(2xt\right)=\sum_{n=0}^{\infty}\frac{H_{2n+1}\left(x\right)}{(2n+1)!}t^{2n+1}}}}$

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
${\displaystyle{\displaystyle{\displaystyle\mathrm{sinh}}}}$ : hyperbolic sine function : http://dlmf.nist.gov/4.28#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : 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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