DLMF:18.28.E18 (Q5993)

No description defined

Language	Label	Description	Also known as
English	DLMF:18.28.E18	No description defined

Statements

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \contqinvHermitepolyh{n}@{\sinh@@{t}}{q}=\sum_{\ell=0}^{n}q^{\frac{1}{2}\ell(\ell+1)}\frac{\qPochhammer{q^{-n}}{q}{\ell}}{\qPochhammer{q}{q}{\ell}}e^{(n-2\ell)t}=e^{nt}\qgenhyperphi{1}{1}@@{q^{-n}}{0}{q}{-qe^{-2t}}=\iunit^{-n}\contqHermitepolyH{n}@{\iunit\sinh@@{t}}{q^{-1}}.}

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DLMF id

DLMF:18.28.E18

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Symbols defined

continuous $$q^{-1}$$ -Hermite polynomial

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Symbols used

continuous $$q$$ -Hermite polynomial

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \contqHermitepolyH{\NVar{n}}@{\NVar{x}}{\NVar{q}}}

xml-id

C18.S28.E16.m2abdec

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base of natural logarithm

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}

xml-id

C4.S2.E11.m2aidec

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hyperbolic sine function

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{\NVar{z}}}

xml-id

C4.S28.E1.m2adec

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imaginary unit

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}

xml-id

C1.S9.E1.m2ajdec

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Q11298

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}}

xml-id

C17.S2.SS1.p1.m2amdec

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basic hypergeometric (or $$q$$ -hypergeometric) function

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{\NVar{r+1}}{\NVar{s}}@{\NVar{a_{0},\dots,a_{r}}}{\NVar{b_{1},\dots,b_{s}}}{\NVar{q}}{\NVar{z}}}

xml-id

C17.S4.E1.m2afdec

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Q11728

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}

xml-id

C18.S1.XMD3.m1odec

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Q11744

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell}