DLMF:14.20.E3 (Q4924)

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Language	Label	Description	Also known as
English	DLMF:14.20.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\mu}_{-\frac{1}{2}+\mathrm{% i}\tau}\left(x\right)=\frac{\pi e^{-\tau\pi}\sin\left(\mu\pi\right)\sinh\left(% \tau\pi\right)}{2({\cosh^{2}}\left(\tau\pi\right)-{\sin^{2}}\left(\mu\pi\right% ))}\mathsf{P}^{-\mu}_{-\frac{1}{2}+\mathrm{i}\tau}\left(x\right)+\frac{\pi(e^{% -\tau\pi}{\cos^{2}}\left(\mu\pi\right)+\sinh\left(\tau\pi\right))}{2({\cosh^{2% }}\left(\tau\pi\right)-{\sin^{2}}\left(\mu\pi\right))}\mathsf{P}^{-\mu}_{-% \frac{1}{2}+\mathrm{i}\tau}\left(-x\right).}}

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DLMF:14.20.E3

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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.m2aadec

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conical function

Defining formula

{\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\NVar{\mu}}_{\NVar{-\frac{1% }{2}+i\tau}}\left(\NVar{x}\right)}}

C14.S20.E2.m2aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aadec

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cosine function

Defining formula

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

C4.S14.E2.m2adec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aadec

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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\mathrm{i}}}

C1.S9.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1bdec

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Sitelinks

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