DLMF:13.21.E13 (Q4621): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.21.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle M_{\kappa,\mu}\left(x\right)=\Gamma\left(2\mu+1% \right)\*\left(\frac{e^{2}}{\kappa^{2}-\mu^{2}}\right)^{\frac{1}{2}\mu}\*\left% (\frac{\kappa-\mu}{\kappa+\mu}\right)^{\frac{1}{2}\kappa}\*\Psi(\kappa,\mu,x)% \*\left(J_{2\mu}\left(\sqrt{\zeta\kappa}\right)+\mathrm{env}\mskip-2.0mu J_{2% \mu}\left(\sqrt{\zeta\kappa}\right)O\left(\kappa^{-1}\right)\right),}}

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DLMF:13.21.E13

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2abdec

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2afdec

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Defining formula

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

C5.S2.E1.m2aedec

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Whittaker confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

C13.S14.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar% {x}\right)}}

C2.S8.SS4.p5.m2aadec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2addec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1kdec

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function (locally)

Defining formula

{\displaystyle{\displaystyle\Psi(\kappa,\mu,x)}}

C13.S21.XMD3.m1adec

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