Formula:5135

Digital Library of Mathematical Functions ID 13.8.E13

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \OlverconfhyperM@{-a}{b}{z}\asympexp\left(z/a\right)^{(1-b)/2}\frac{e^{z/2}\EulerGamma@{1+a}}{\EulerGamma@{a+b}}\*\left(\BesselJ{b-1}@{2\sqrt{az}}\sum_{s=0}^{\infty}\frac{p_{s}(z)}{(-a)^{s}}-\sqrt{z/a}\BesselJ{b}@{2\sqrt{az}}\sum_{s=0}^{\infty}\frac{q_{s}(z)}{(-a)^{s}}\right),}

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$: Olver’s confluent hypergeometric function
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle s}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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