Formula:KLS:14.10:53

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Substitution(s)

&

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle w(x):=w(x;\beta|q) =\left|\frac{\qPochhammer{\expe^{2\iunit\theta}}{q}{\infty}} {\qPochhammer{\beta^{\frac{1}{2}}\expe^{\iunit\theta},\beta^{\frac{1}{2}}q^{\frac{1}{2}}\expe^{\iunit\theta} -\beta^{\frac{1}{2}}\expe^{\iunit\theta},-\beta^{\frac{1}{2}}q^{\frac{1}{2}}\expe^{\iunit\theta}}{q}{\infty}}\right|^2 =\left|\frac{\qPochhammer{\expe^{2\iunit\theta}}{q}{\infty}}{\qPochhammer{\beta\expe^{2\iunit\theta}}{q}{\infty}}\right|^2 =\frac{h(x,1)h(x,-1)h(x,q^{\frac{1}{2}})h(x,-q^{\frac{1}{2}})} {h(x,\beta^{\frac{1}{2}})h(x,\beta^{\frac{1}{2}}q^{\frac{1}{2}}) h(x,-\beta^{\frac{1}{2}})h(x,-\beta^{\frac{1}{2}}q^{\frac{1}{2}})}}} &
&


Proof

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Symbols List

& : logical and
 : continuous -ultraspherical/Rogers polynomial : http://dlmf.nist.gov/18.28#E13
 : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
 : imaginary unit : http://dlmf.nist.gov/1.9.i
 : -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
 : product : http://drmf.wmflabs.org/wiki/Definition:prod
 : cosine function : http://dlmf.nist.gov/4.14#E2

Bibliography

Equation in Section 14.10 of KLS.

URL links

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