Formula:4822

Digital Library of Mathematical Functions ID 12.7.E2

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \paraU@{-n-\tfrac{1}{2}}{z}=\WhittakerparaD{n}@{z}=e^{-\frac{1}{4}z^{2}}\dilHermitepolyHe{n}@{z}=2^{-n/2}e^{-\frac{1}{4}z^{2}}\HermitepolyH{n}@{z/\sqrt{2}},}

Constraint(s)

${\displaystyle{\displaystyle n=0,1,2,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle\mathit{He}_{\NVar{n}}\left(\NVar{x}\right)}}$: Hermite polynomial
• ${\displaystyle{\displaystyle D_{\NVar{\nu}}\left(\NVar{z}\right)}}$: parabolic cylinder function
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \expe} : base of natural logarithm
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \paraU@{\NVar{a}}{\NVar{z}}} :
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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