DLMF:13.16.E8 (Q4559): Difference between revisions

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Latest revision as of 16:11, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:13.16.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{2\sqrt{z}e^{-% \frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2% }-\mu-\kappa\right)}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}K_{2\mu}% \left(2\sqrt{zt}\right)\mathrm{d}t,}}

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DLMF:13.16.E8

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{\displaystyle{\displaystyle\Re(\mu-\kappa)+\tfrac{1}{2}>0}}

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Defining formula

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

C5.S2.E1.m2agdec

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Defining formula

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

C1.S4.SS4.m1agdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2agdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3agdec

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modified Bessel function of the second kind

Defining formula

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

C10.S25.E3.m2adec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1agdec

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Defining formula

{\displaystyle{\displaystyle z}}

C13.S1.XMD6.m1gdec

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E3.m2acdec

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