DLMF:14.18.E4 (Q4905)

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Language	Label	Description	Also known as
English	DLMF:14.18.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P_{\nu}\left(\cosh\xi_{1}\cosh\xi_{2}-\sinh\xi_{1% }\sinh\xi_{2}\cos\phi\right)=P_{\nu}\left(\cosh\xi_{1}\right)P_{\nu}\left(% \cosh\xi_{2}\right)+2\sum_{m=1}^{\infty}(-1)^{m}P^{-m}_{\nu}\left(\cosh\xi_{1}% \right)P^{m}_{\nu}\left(\cosh\xi_{2}\right)\cos\left(m\phi\right),}}

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DLMF:14.18.E4

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Defining formula

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

C14.S21.SS1.p1.m1adec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2acdec

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hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2adec

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hyperbolic sine function

Defining formula

{\displaystyle{\displaystyle\sinh\NVar{z}}}

C4.S28.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}

C14.S2.SS2.p2.m3adec

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Defining formula

{\displaystyle{\displaystyle m}}

C14.S1.XMD5.m1cdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1bdec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C14.S18.XMD2.m1cdec

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Defining formula

{\displaystyle{\displaystyle\xi_{1}}}

C14.S18.XMD3.m1dec

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Sitelinks

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