Definition:GenHermite

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The LaTeX DLMF and DRMF macro \GenHermite represents the generalized Hermite polynomial.

This macro is in the category of polynomials.

In math mode, this macro can be called in the following ways:

\GenHermite[\alpha]{n} produces Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \GenHermite[\alpha]{n}}}
\GenHermite{n} produces Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \GenHermite{n}}}
\GenHermite[\alpha]{n}@{x} produces Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \GenHermite[\alpha]{n}@{x}}}
\GenHermite{n}@{x} produces Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \GenHermite{n}@{x}}}

These are defined by

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle \GenHermite[\mu]{2m}@{x}:={\rm const}\times \Laguerre[\mu-\frac12]{m}@{x^2},\qquad }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle \GenHermite[\mu]{2m+1}@{x}:={\rm \const}\times x \Laguerre[\mu+\frac12]{m}@{x^2}. }
Then for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle \mu>-\tfrac12} we have orthogonality relation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle \int_{-\infty}^{\infty} \GenHermite[\mu]{m}@{x} \GenHermite[\mu]{n}@{x} |x|^{2\mu}e^{-x^2} dx, =0 }
for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle m\ne n} .

Bibliography


Page 156 of CHI.

Symbols List

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle H_n^{\mu}}}  : generalized Hermite polynomial : http://drmf.wmflabs.org/wiki/Definition:GenHermite
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle L_n^{(\alpha)}}}  : Laguerre (or generalized Laguerre) polynomial : http://dlmf.nist.gov/18.3#T1.t1.r27
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \int}}  : integral : http://dlmf.nist.gov/1.4#iv