DLMF:13.16.E6 (Q4557): 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.E6	No description defined

Statements

Defining formula

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

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DLMF:13.16.E6

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{\displaystyle{\displaystyle|\operatorname{ph}{z}|<\pi}}

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{\displaystyle{\displaystyle\Re(\frac{1}{2}+\mu-\kappa)>\max\left(2\Re\mu,0% \right)}}

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E3.m2aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aadec

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Defining formula

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

C1.S4.SS4.m1aedec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aedec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aedec

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Defining formula

{\displaystyle{\displaystyle\operatorname{ph}}}

C1.S9.E7.m1aadec

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Defining formula

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

C5.S2.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle z}}

C13.S1.XMD6.m1edec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aedec

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