DLMF:13.4.E12 (Q4375)

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Language	Label	Description	Also known as
English	DLMF:13.4.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\mathbf{M}}\left(a,c,z\right)=\frac{\Gamma\left(b% \right)}{2\pi\mathrm{i}}z^{1-b}\int_{-\infty}^{(0+,1+)}e^{zt}t^{-b}{{}_{2}{% \mathbf{F}}_{1}}\left(a,b;c;\ifrac{1}{t}\right)\mathrm{d}t,}}

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DLMF:13.4.E12

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{\displaystyle{\displaystyle\left|\operatorname{ph}z\right|<\frac{1}{2}\pi}}

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{\displaystyle{\displaystyle b\neq 0,-1,-2,\dots}}

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{\displaystyle{\displaystyle\left|\operatorname{ph}z\right|<\frac{1}{2}\pi}}

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Defining formula

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

C5.S2.E1.m2ajdec

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Olver’s confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}

C13.S2.E3.m2agdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2agdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1akdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2ajdec

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scaled (or Olver’s) generalized hypergeometric function

Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{% \mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}

C16.S2.E5.m2aadec

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Defining formula

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

C1.S9.E1.m2acdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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