DLMF:14.3.E20 (Q4709)

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Language	Label	Description	Also known as
English	DLMF:14.3.E20	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{2\sin\left(\mu\pi\right)}{\pi}\boldsymbol{Q}% ^{\mu}_{\nu}\left(x\right)=\frac{(x+1)^{\mu/2}}{\Gamma\left(\nu+\mu+1\right)(x% -1)^{\mu/2}}\mathbf{F}\left(\nu+1,-\nu;1-\mu;\tfrac{1}{2}-\tfrac{1}{2}x\right)% -\frac{(x-1)^{\mu/2}}{\Gamma\left(\nu-\mu+1\right)(x+1)^{\mu/2}}\mathbf{F}% \left(\nu+1,-\nu;\mu+1;\tfrac{1}{2}-\tfrac{1}{2}x\right).}}

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DLMF:14.3.E20

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Defining formula

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

C5.S2.E1.m2aldec

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Defining formula

{\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}

C14.S21.SS1.p1.m3abdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2agdec

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$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}

C15.S2.E2.m2apdec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1sdec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1odec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1rdec

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Sitelinks

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