DLMF:13.8.E4 (Q4429)

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Language	Label	Description	Also known as
English	DLMF:13.8.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle M\left(a,b,z\right)\sim b^{\frac{1}{2}a}e^{\frac{% 1}{4}\zeta^{2}b}\left(\lambda\left(\frac{\lambda-1}{\zeta}\right)^{a-1}U\left(% a-\tfrac{1}{2},-\zeta\sqrt{b}\right)+\left(\lambda\left(\frac{\lambda-1}{\zeta% }\right)^{a-1}-\left(\frac{\zeta}{\lambda-1}\right)^{a}\right)\frac{U\left(a-% \tfrac{3}{2},-\zeta\sqrt{b}\right)}{\zeta\sqrt{b}}\right)}}

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DLMF:13.8.E4

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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.m2abdec

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asymptotic equality

Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.E1.m2adec

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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 U\left(\NVar{a},\NVar{z}\right)}}

C12.S2.SS1.p1.m1adec

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Defining formula

{\displaystyle{\displaystyle z}}

C13.S1.XMD6.m1cdec

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