DLMF:13.14.E6 (Q4495): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.14.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{% \frac{1}{2}+\mu}\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_% {s}}}{{\left(1+2\mu\right)_{s}}s!}z^{s}=z^{\frac{1}{2}+\mu}\sum_{n=0}^{\infty}% {{}_{2}F_{1}}\left({-n,\tfrac{1}{2}+\mu-\kappa\atop 1+2\mu};2\right)\frac{% \left(-\tfrac{1}{2}z\right)^{n}}{n!},}}

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DLMF:13.14.E6

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{\displaystyle{\displaystyle 2\mu\neq-1,-2,-3,\dots}}

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Defining formula

{\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

C16.S2.m5adec

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Defining formula

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

C5.S2.SS3.m1adec

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E2.m2abdec

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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!}}

introduction.Sx4.p1.t1.r15.m5adec

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Defining formula

{\displaystyle{\displaystyle n}}

C13.S1.XMD2.m1dec

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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.m1edec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2addec

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Sitelinks

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