Formula:5010

Digital Library of Mathematical Functions ID 13.2.E23

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \OlverconfhyperM@{a}{b}{z}\asympeq\ifrac{e^{z}z^{a-b}}{\EulerGamma@{a}},}

Constraint(s)

${\displaystyle{\displaystyle\left|\operatorname{ph}z\right|\leq\frac{1}{2}\pi-\delta}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$: Olver’s confluent hypergeometric function
• ${\displaystyle{\displaystyle\sim}}$: asymptotic equality
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\delta}}$: small positive constant
 

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