Formula:5098

Digital Library of Mathematical Functions ID 13.6.E14

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \KummerconfhyperM@{\tfrac{1}{2}a+\tfrac{1}{4}}{\tfrac{1}{2}}{\tfrac{1}{2}z^{2}}=\frac{2^{\frac{1}{2}a-\frac{3}{4}}\EulerGamma@{\tfrac{1}{2}a+\tfrac{3}{4}}e^{\frac{1}{4}z^{2}}}{\sqrt{\pi}}\*\left(\paraU@{a}{z}+\paraU@{a}{-z}\right),}

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: 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
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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