DLMF:14.20.E22 (Q4943): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:14.20.E22	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{-\frac{1}{2}+i\tau}\left(x% \right)=\frac{\beta\exp\left(\mu\beta\operatorname{arctan}\beta\right)}{\Gamma% \left(\mu+1\right)\left(1+\beta^{2}\right)^{\mu/2}}\frac{e^{-\mu\rho}}{\left(1% +\beta^{2}-x^{2}\beta^{2}\right)^{1/4}}\left(1+O\left(\frac{1}{\mu}\right)% \right),}}

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DLMF:14.20.E22

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order not exceeding

Defining formula

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

C2.S1.E3.m2addec

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Defining formula

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

C5.S2.E1.m2afdec

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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.m2ajdec

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exponential function

Defining formula

{\displaystyle{\displaystyle\exp\NVar{z}}}

C4.S2.E19.m2aadec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2aedec

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Defining formula

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

C1.S9.E1.m2aydec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

C4.S23.SS2.p1.m7aadec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1wdec

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Defining formula

{\displaystyle{\displaystyle\tau}}

C14.S1.XMD3.m1abdec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1pdec

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Sitelinks

Wikipedia(0 entries)

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