DLMF:14.20.E6 (Q4927)

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Language	Label	Description	Also known as
English	DLMF:14.20.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P^{-\mu}_{-\frac{1}{2}+i\tau}\left(x\right)=\frac% {ie^{-\mu\pi i}}{\sinh\left(\tau\pi\right)\left|\Gamma\left(\mu+\frac{1}{2}+i% \tau\right)\right|^{2}}\*\left(Q^{\mu}_{-\frac{1}{2}+i\tau}\left(x\right)-Q^{% \mu}_{-\frac{1}{2}-i\tau}\left(x\right)\right),}}

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DLMF:14.20.E6

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{\displaystyle{\displaystyle\tau\neq 0}}

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Defining formula

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

C5.S2.E1.m2abdec

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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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Defining formula

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

C14.S21.SS1.p1.m2adec

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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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hyperbolic sine function

Defining formula

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

C4.S28.E1.m2abdec

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Defining formula

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

C1.S9.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1edec

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