DLMF:13.23.E10 (Q4644)

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Language	Label	Description	Also known as
English	DLMF:13.23.E10	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{% \infty}e^{-\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}M_{\kappa,\mu}\left(t\right)% J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\frac{e^{-\frac{1}{2}x}x^{\frac{1}{2% }(\kappa+\mu-\frac{3}{2})}}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}\*W_{% \frac{1}{2}(\kappa-3\mu+\nu+\frac{1}{2}),\frac{1}{2}(\kappa+\mu-\nu-\frac{1}{2% })}\left(x\right),}}

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DLMF:13.23.E10

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{\displaystyle{\displaystyle-1<\Re\nu<2\Re(\mu+\kappa)+\tfrac{1}{2}}}

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{\displaystyle{\displaystyle x>0}}

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{\displaystyle{\displaystyle-1<\Re\nu<2\Re(\mu+\kappa)+\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.m2aadec

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