DLMF:13.8.E13 (Q4438)

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Language	Label	Description	Also known as
English	DLMF:13.8.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\mathbf{M}}\left(-a,b,z\right)\sim\left(z/a\right% )^{(1-b)/2}\frac{e^{z/2}\Gamma\left(1+a\right)}{\Gamma\left(a+b\right)}\*\left% (J_{b-1}\left(2\sqrt{az}\right)\sum_{s=0}^{\infty}\frac{p_{s}(z)}{(-a)^{s}}-% \sqrt{z/a}J_{b}\left(2\sqrt{az}\right)\sum_{s=0}^{\infty}\frac{q_{s}(z)}{(-a)^% {s}}\right),}}

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DLMF:13.8.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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Defining formula

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

C5.S2.E1.m2ahdec

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Olver’s confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}

C13.S2.E3.m2aadec

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Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11acdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2ahdec

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Defining formula

{\displaystyle{\displaystyle s}}

C13.S1.XMD3.m1edec

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Defining formula

{\displaystyle{\displaystyle z}}

C13.S1.XMD6.m1gdec

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