DLMF:10.22.E48 (Q3422)

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Language	Label	Description	Also known as
English	DLMF:10.22.E48	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}J_{\mu}\left(x\cosh\phi\right)(% \cosh\phi)^{1-\mu}(\sinh\phi)^{2\nu+1}\mathrm{d}\phi=2^{\nu}\Gamma\left(\nu+1% \right)x^{-\nu-1}J_{\mu-\nu-1}\left(x\right),}}

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DLMF:10.22.E48

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{\displaystyle{\displaystyle x>0,\Re\nu>-1,\Re\mu>2\Re\nu+\tfrac{1}{2}}}

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Bessel function of the first kind

Defining formula

{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E2.m2aajdec

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Defining formula

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

C5.S2.E1.m2amdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1aaudec

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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\int}}

C1.S4.SS4.m3aaudec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aacdec

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Defining formula

{\displaystyle{\displaystyle x}}

C10.S1.XMD4.m1qdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1agdec

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