DLMF:14.24.E4 (Q4957)

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Language	Label	Description	Also known as
English	DLMF:14.24.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu,s}\left(z\right)=e^{-s% \mu\pi i}\boldsymbol{Q}^{\mu}_{\nu}\left(z\right)-\frac{\pi i\sin\left(s\mu\pi% \right)}{\sin\left(\mu\pi\right)\Gamma\left(\nu-\mu+1\right)}P^{-\mu}_{\nu}% \left(z\right),}}

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DLMF:14.24.E4

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Defining formula

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

C5.S2.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

C14.S21.SS1.p1.m1abdec

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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.m2acdec

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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\sin\NVar{z}}}

C4.S14.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle z}}

C14.S1.XMD4.m1cdec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1cdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1cdec

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Defining formula

{\displaystyle{\displaystyle s}}

C14.S24.XMD1.m1cdec

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