DLMF:13.19.E2 (Q4588): Difference between revisions

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English	DLMF:13.19.E2	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)\sim\frac{\Gamma\left% (1+2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}e^{\frac{1}{2}z}z^{-% \kappa}\*\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}-\mu+\kappa\right)_{s}}{% \left(\frac{1}{2}+\mu+\kappa\right)_{s}}}{s!}z^{-s}+\frac{\Gamma\left(1+2\mu% \right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}e^{-\frac{1}{2}z\pm(\frac{1% }{2}+\mu-\kappa)\pi\mathrm{i}}z^{\kappa}\*\sum_{s=0}^{\infty}\frac{{\left(% \frac{1}{2}+\mu-\kappa\right)_{s}}{\left(\frac{1}{2}-\mu-\kappa\right)_{s}}}{s% !}(-z)^{-s},}}

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DLMF:13.19.E2

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{\displaystyle{\displaystyle-\tfrac{1}{2}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{3}{2}\pi-\delta}}

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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.m1aadec

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Whittaker confluent hypergeometric function

Defining formula

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

C13.S14.E2.m2aadec

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Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.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!}}

introduction.Sx4.p1.t1.r15.m5aadec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\operatorname{ph}}}

C1.S9.E7.m1adec

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Defining formula

{\displaystyle{\displaystyle s}}

C13.S1.XMD3.m1adec

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