DLMF:13.8.E9 (Q4434): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.8.E9	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle M\left(a,b,x\right)=\Gamma\left(b\right)e^{\frac{% 1}{2}x}\left((\tfrac{1}{2}b-a)x\right)^{\frac{1}{2}-\frac{1}{2}b}\*\left(J_{b-% 1}\left(\sqrt{2x(b-2a)}\right)+\mathrm{env}\mskip-2.0mu J_{b-1}\left(\sqrt{2x(% b-2a)}\right)O\left({\left|a\right|^{-\frac{1}{2}}}\right)\right),}}

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DLMF:13.8.E9

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2adec

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2addec

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Defining formula

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

C5.S2.E1.m2addec

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$$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function

Defining formula

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

C13.S2.E2.m2addec

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Defining formula

{\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar% {x}\right)}}

C2.S8.SS4.p5.m2adec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2addec

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