DLMF:18.27.E20 (Q5971): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:18.27.E20	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}S_{n}\left(q^{\frac{1}{2}}x;q% \right)S_{m}\left(q^{\frac{1}{2}}x;q\right)\exp\left(-\frac{(\ln x)^{2}}{2\ln% \left(q^{-1}\right)}\right)\mathrm{d}x=\frac{\sqrt{2\pi q^{-1}\ln\left(q^{-1}% \right)}}{q^{n}\left(q;q\right)_{n}}\delta_{n,m}.}}

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DLMF:18.27.E20

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Defining formula

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

introduction.Sx4.p1.t1.r4.m5afdec

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Stieltjes–Wigert polynomial

Defining formula

{\displaystyle{\displaystyle S_{\NVar{n}}\left(\NVar{x};\NVar{q}\right)}}

C18.S27.E18.m2abdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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Defining formula

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

C1.S4.SS4.m1abdec

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exponential function

Defining formula

{\displaystyle{\displaystyle\exp\NVar{z}}}

C4.S2.E19.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abdec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2aadec

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Defining formula

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

C17.S2.SS1.p1.m2afdec

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Defining formula

{\displaystyle{\displaystyle q}}

C18.S1.XMD3.m1rdec

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Defining formula

{\displaystyle{\displaystyle m}}

C18.S1.XMD5.m1fdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1odec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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