DLMF:13.24.E1 (Q4649): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.24.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\Gamma\left(\kappa+% \mu\right)2^{2\kappa+2\mu}z^{\frac{1}{2}-\kappa}\*\sum_{s=0}^{\infty}(-1)^{s}% \frac{{\left(2\kappa+2\mu\right)_{s}}{\left(2\kappa\right)_{s}}}{{\left(1+2\mu% \right)_{s}}s!}\*\left(\kappa+\mu+s\right)I_{\kappa+\mu+s}\left(\tfrac{1}{2}z% \right),}}

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DLMF:13.24.E1

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{\displaystyle{\displaystyle 2\mu,\kappa+\mu\neq-1,-2,-3,\dots}}

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Defining formula

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

C5.S2.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1adec

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5adec

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modified Bessel function of the first kind

Defining formula

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

C10.S25.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle s}}

C13.S1.XMD3.m1dec

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Defining formula

{\displaystyle{\displaystyle z}}

C13.S1.XMD6.m1dec

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