DLMF:14.15.E25 (Q4872)

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Language	Label	Description	Also known as
English	DLMF:14.15.E25	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathsf{Q}^{-\mu}_{\nu}\left(x\right)=\frac{\pi}{% \left(\nu+\frac{1}{2}\right)^{1/4}2^{(\nu+\mu+2)/2}\Gamma\left(\frac{1}{2}\nu+% \frac{1}{2}\mu+\frac{3}{4}\right)}\*\left(\frac{\zeta^{2}-\alpha^{2}}{x^{2}-a^% {2}}\right)^{1/4}\*\left(\overline{U}\left(\mu-\nu-\tfrac{1}{2},\left(2\nu+1% \right)^{1/2}\zeta\right)+O\left(\nu^{-2/3}\right)\mathrm{env}\mskip-1.0mu % \overline{U}\left(\mu-\nu-\tfrac{1}{2},\left(2\nu+1\right)^{1/2}\zeta\right)% \right),}}

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DLMF:14.15.E25

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2aodec

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2agdec

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Ferrers function of the second kind

Defining formula

{\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C14.S3.E2.m2abdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2afdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu \overline{U}\left(\NVar{c% },\NVar{x}\right)}}

C14.S15.SS5.p1.m9aadec

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Defining formula

{\displaystyle{\displaystyle\overline{U}\left(\NVar{a},\NVar{x}\right)}}

C12.S2.SS6.p1.m4aadec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1pdec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1rdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1rdec

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Defining formula

{\displaystyle{\displaystyle a}}

C14.S15.XMD13.m1adec

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Defining formula

{\displaystyle{\displaystyle\zeta}}

C14.S15.XMD14.m1adec

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Sitelinks

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