DLMF:13.20.E17 (Q4606): Difference between revisions

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Latest revision as of 14:16, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:13.20.E17	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle M_{\kappa,\mu}\left(x\right)=\left(8\mu\right)^{% \frac{1}{4}}\*\left(\frac{2\mu}{e}\right)^{2\mu}\*\left(\frac{e}{\kappa+\mu}% \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 \overline{U}\left(\mu-% \kappa,\zeta\sqrt{2\mu}\right)O\left(\mu^{-\frac{2}{3}}\right)\right),}}

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DLMF:13.20.E17

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order not exceeding

Defining formula

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

C2.S1.E3.m2agdec

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E2.m2acdec

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Defining formula

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

C14.S15.SS5.p1.m9adec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aedec

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Defining formula

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

C12.S2.SS1.p1.m1acdec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1ndec

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function (locally)

Defining formula

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

C13.S20.XMD4.m1ddec

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