DLMF:13.11.E1 (Q4476)

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Language	Label	Description	Also known as
English	DLMF:13.11.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle M\left(a,b,z\right)=\Gamma\left(a-\tfrac{1}{2}% \right)e^{\frac{1}{2}z}\left(\tfrac{1}{4}z\right)^{\frac{1}{2}-a}\*\sum_{s=0}^% {\infty}\frac{{\left(2a-1\right)_{s}}{\left(2a-b\right)_{s}}}{{\left(b\right)_% {s}}s!}\*\left(a-\tfrac{1}{2}+s\right)\*I_{a-\frac{1}{2}+s}\left(\tfrac{1}{2}z% \right),}}

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DLMF:13.11.E1

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{\displaystyle{\displaystyle a+\frac{1}{2},b\neq 0,-1,-2,\dots}}

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Defining formula

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

C5.S2.E1.m2adec

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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.m2adec

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Defining formula

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

C5.S2.SS3.m1adec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2adec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5adec

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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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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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