DLMF:14.3.E23 (Q4712)

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Language	Label	Description	Also known as
English	DLMF:14.3.E23	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P^{\mu}_{\nu}\left(x\right)=\frac{1}{\Gamma\left(% 1-\mu\right)}\left(\frac{x+1}{x-1}\right)^{\mu/2}\phi^{(-\mu,\mu)}_{-\mathrm{i% }(2\nu+1)}\left(\operatorname{arcsinh}\left((\tfrac{1}{2}x-\tfrac{1}{2})^{% \ifrac{1}{2}}\right)\right).}}

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DLMF:14.3.E23

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Defining formula

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

C5.S2.E1.m2aodec

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Jacobi function

Defining formula

{\displaystyle{\displaystyle\phi^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{\lambda% }}\left(\NVar{t}\right)}}

C15.S9.E11.m2adec

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Defining formula

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

C14.S21.SS1.p1.m1ahdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}

C4.S37.SS2.p1.m8adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2abdec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1vdec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1rdec

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Sitelinks

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