Formula:5128

Digital Library of Mathematical Functions ID 13.8.E6

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \KummerconfhyperM@{a}{b}{b}=\sqrt{\pi}\left(\frac{b}{2}\right)^{\frac{1}{2}a}\left(\frac{1}{\EulerGamma@{\frac{1}{2}(a+1)}}+\frac{(a+1)\sqrt{8/b}}{3\EulerGamma@{\frac{1}{2}a}}+\bigO@{\frac{1}{b}}\right),}

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
 

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