Formula:KLS:14.21:31

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{h_n}{h_0}=\frac{\qPochhammer{q^{\alpha+1}}{q}{n}}{\qPochhammer{q}{q}{n} q^n},\qquad h_0 }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \frac{h_n}{h_0} =- \frac{\qPochhammer{q^{-\alpha}}{q}{\infty}}{\qPochhammer{q}{q}{\infty}} \frac\cpi{\sin@{\cpi\alpha}}}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle h_n=q^{-\frac12\alpha(\alpha+1)} \qPochhammer{q}{q}{\alpha} \log(q^{-1})\qquad(\alpha\in\ZZ_{\ge0})}}


Proof

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Symbols List

& : logical and
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a;q)_n}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{sin}}}  : sine function : http://dlmf.nist.gov/4.14#E1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \pi}}  : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{log}}}  : principle branch of logarithm logarithm : http://dlmf.nist.gov/4.2#E2

Bibliography

Equation in Section 14.21 of KLS.

URL links

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