DLMF:14.15.E30 (Q4878)

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Language	Label	Description	Also known as
English	DLMF:14.15.E30	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{\nu}\left(x\right)=\frac{1}{% \left(\nu+\frac{1}{2}\right)^{1/4}2^{(\nu+\mu)/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}\*U\left(\mu-\nu-\tfrac{1}{2},\left(2\nu+1\right)^{1/2}\zeta% \right)\left(1+O\left(\nu^{-1}\ln\nu\right)\right),}}

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DLMF:14.15.E30

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order not exceeding

Defining formula

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

C2.S1.E3.m2apdec

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Defining formula

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

C5.S2.E1.m2ahdec

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Ferrers function of the first kind

Defining formula

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

C14.S3.E1.m2aedec

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principal branch of logarithm function

Defining formula

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

C4.S2.E2.m2addec

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Defining formula

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

C12.S2.SS1.p1.m1abdec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1tdec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1tdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1tdec

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Defining formula

{\displaystyle{\displaystyle a}}

C14.S15.XMD13.m1edec

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Defining formula

{\displaystyle{\displaystyle\zeta}}

C14.S15.XMD14.m1edec

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Defining formula

{\displaystyle{\displaystyle\alpha}}

C14.S15.XMD9.m1ldec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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