Formula:KLS:09.15:12

<< Formula:KLS:09.15:11

formula in Hermite

Formula:KLS:09.15:13 >>

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

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
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : 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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