DLMF:13.20.E16 (Q4605)

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Language	Label	Description	Also known as
English	DLMF:13.20.E16	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\left(\tfrac{1}{2}% \mu\right)^{-\frac{1}{4}}\*\left(\frac{\kappa+\mu}{e}\right)^{\frac{1}{2}(% \kappa+\mu)}\*\Phi(\kappa,\mu,x)\*\left(U\left(\mu-\kappa,\zeta\sqrt{2\mu}% \right)+\mathrm{env}\mskip-1.0mu U\left(\mu-\kappa,\zeta\sqrt{2\mu}\right)O% \left(\mu^{-\frac{2}{3}}\right)\right),}}

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DLMF:13.20.E16

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order not exceeding

Defining formula

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

C2.S1.E3.m2afdec

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E3.m2acdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu U\left(\NVar{c},\NVar{x}% \right)}}

C14.S15.SS5.p1.m7adec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2addec

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Defining formula

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

C12.S2.SS1.p1.m1abdec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1mdec

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function (locally)

Defining formula

{\displaystyle{\displaystyle\Phi(\kappa,\mu,x)}}

C13.S20.XMD4.m1cdec

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