Formula:5134

Digital Library of Mathematical Functions ID 13.8.E12

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

Symbols List

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

Resources that cite this formula

No records found.