DLMF:14.19.E6 (Q4919)

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Language	Label	Description	Also known as
English	DLMF:14.19.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{-\frac{1}{2}}\left(\cosh\xi% \right)+2\sum_{n=1}^{\infty}\frac{\Gamma\left(\mu+n+\tfrac{1}{2}\right)}{% \Gamma\left(\mu+\tfrac{1}{2}\right)}\boldsymbol{Q}^{\mu}_{n-\frac{1}{2}}\left(% \cosh\xi\right)\cos\left(n\phi\right)=\dfrac{\left(\frac{1}{2}\pi\right)^{1/2}% \left(\sinh\xi\right)^{\mu}}{\left(\cosh\xi-\cos\phi\right)^{\mu+(1/2)}},}}

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DLMF:14.19.E6

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{\displaystyle{\displaystyle\Re\mu>-\tfrac{1}{2}}}

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Defining formula

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

C5.S2.E1.m2acdec

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Defining formula

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

C14.S21.SS1.p1.m3abdec

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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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cosine function

Defining formula

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

C4.S14.E2.m2abdec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2aedec

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hyperbolic sine function

Defining formula

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

C4.S28.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1adec

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