Formula:5073

Digital Library of Mathematical Functions ID 13.4.E13

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \OlverconfhyperM@{a}{b}{z}=\frac{z^{1-b}}{2\pi\iunit}\int_{-\infty}^{(0+,1+)}e^{zt}t^{-b}\!\left(1-\frac{1}{t}\right)^{-a}\diff{t},}

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$: Olver’s confluent hypergeometric function
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \cpi} : the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \expe} : base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}$:
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \phase} : phase
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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