Formula:4849

Digital Library of Mathematical Functions ID 12.9.E3

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \paraU@{a}{z}\asympexp e^{-\frac{1}{4}z^{2}}z^{-a-\frac{1}{2}}\sum_{s=0}^{\infty}(-1)^{s}\frac{\Pochhammersym{\frac{1}{2}+a}{2s}}{s!(2z^{2})^{s}}\pm i\frac{\sqrt{2\pi}}{\EulerGamma@{\tfrac{1}{2}+a}}e^{\mp i\pi a}e^{\frac{1}{4}z^{2}}z^{a-\frac{1}{2}}\sum_{s=0}^{\infty}\frac{\Pochhammersym{\tfrac{1}{2}-a}{2s}}{s!(2z^{2})^{s}},}

Constraint(s)

${\displaystyle{\displaystyle\tfrac{1}{4}\pi+\delta\leq\pm\operatorname{ph}z\leq\tfrac{5}{4}\pi-\delta}}$

Symbols List

• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \EulerGamma@{\NVar{z}}} : gamma function
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle\sim}}$:
• 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
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \expe} : base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \iunit} : imaginary unit
• ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$:
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \phase} : phase
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle s}}$: nonnegative integer
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle\delta}}$: arbitrary small positive constant
 

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