DLMF:13.23.E2 (Q4636): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.23.E2	No description defined

Statements

Defining formula

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

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DLMF:13.23.E2

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{\displaystyle{\displaystyle\Re\mu>-\tfrac{1}{2}}}

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{\displaystyle{\displaystyle\Re z>\tfrac{1}{2}}}

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Defining formula

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

C5.S2.E1.m2aadec

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E2.m2aadec

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Defining formula

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

C1.S4.SS4.m1aadec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aadec

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