DLMF:13.8.E11

MaRDI QIDQ5133

• Label: DLMF:13.8.E11

Digital Library of Mathematical Functions ID 13.8.E11

${\displaystyle{\displaystyle U\left(a,b,z\right)\sim 2\left(z/a\right)^{(1-b)/2}\frac{e^{z/2}}{\Gamma\left(a\right)}\*\left(K_{b-1}\left(2\sqrt{az}\right)\sum_{s=0}^{\infty}\frac{p_{s}(z)}{a^{s}}+\sqrt{z/a}K_{b}\left(2\sqrt{az}\right)\sum_{s=0}^{\infty}\frac{q_{s}(z)}{a^{s}}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$: Kummer confluent hypergeometric function
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle s}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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