DLMF:18.28.E8 (Q5983)

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Language	Label	Description	Also known as
English	DLMF:18.28.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{1}{2\pi}\int_{0}^{\pi}Q_{n}\left(\cos\theta;% a,b\,|\,q\right)Q_{m}\left(\cos\theta;a,b\,|\,q\right)\*{\left|\frac{\left(e^{% 2i\theta};q\right)_{\infty}}{\left(ae^{i\theta},be^{i\theta};q\right)_{\infty}% }\right|^{2}}\mathrm{d}\theta=\frac{\delta_{n,m}}{\left(q^{n+1},abq^{n};q% \right)_{\infty}},}}

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DLMF:18.28.E8

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{\displaystyle{\displaystyle a,b\in\mathbb{R}}}

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{\displaystyle{\displaystyle a=\overline{b}}}

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{\displaystyle{\displaystyle a=\overline{b}}}

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{\displaystyle{\displaystyle|ab|<1}}

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{\displaystyle{\displaystyle|a|,|b|\leq 1}}

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Al-Salam–Chihara polynomial

Defining formula

{\displaystyle{\displaystyle Q_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b}\,|\,% \NVar{q}\right)}}

C18.S28.E7.m2aadec

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Defining formula

{\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}

introduction.Sx4.p1.t1.r4.m5abdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aadec

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complex conjugate

Defining formula

{\displaystyle{\displaystyle\overline{\NVar{z}}}}

C1.S9.E11.m2adec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2acdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1abdec

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Defining formula

{\displaystyle{\displaystyle\in}}

introduction.Sx4.p1.t1.r10.m2adec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2acdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abdec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

C17.S2.SS1.p1.m2aedec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}

C17.S2.SS1.p1.m6addec

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Defining formula

{\displaystyle{\displaystyle\mathbb{R}}}

introduction.Sx4.p2.t1.r14.m2adec

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Defining formula

{\displaystyle{\displaystyle q}}

C18.S1.XMD3.m1edec

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Defining formula

{\displaystyle{\displaystyle m}}

C18.S1.XMD5.m1bdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1edec

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Sitelinks

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DRMF related sites(0 entries)

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