DLMF:13.14.E8 (Q4497): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.14.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle W_{\kappa,\pm\frac{1}{2}n}\left(z\right)=\frac{(-% 1)^{n}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}}{n!\Gamma\left(\frac{1}{2}% -\frac{1}{2}n-\kappa\right)}\left(\sum_{k=1}^{n}\frac{n!(k-1)!}{(n-k)!{\left(% \kappa+\frac{1}{2}-\frac{1}{2}n\right)_{k}}}z^{-k}-\sum_{k=0}^{\infty}\frac{{% \left(\frac{1}{2}n+\frac{1}{2}-\kappa\right)_{k}}}{{\left(n+1\right)_{k}}k!}z^% {k}\left(\ln z+\psi\left(\tfrac{1}{2}n+\tfrac{1}{2}-\kappa+k\right)-\psi\left(% 1+k\right)-\psi\left(n+1+k\right)\right)\right),}}

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DLMF:13.14.E8

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{\displaystyle{\displaystyle\kappa-\frac{1}{2}n-\frac{1}{2}\neq 0,1,2,\dots}}

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Defining formula

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

C5.S2.E1.m2aadec

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Defining formula

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

C5.S2.SS3.m1abdec

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E3.m2abdec

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psi (or digamma) function

Defining formula

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

C5.S2.E2.m2adec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2afdec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5abdec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2adec

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E3.m2abdec

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Sitelinks

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