Formula:10228

Digital Library of Mathematical Functions ID 33.6.E4

${\displaystyle{\displaystyle A_{k}^{\ell}(\eta)=\dfrac{(-\mathrm{i})^{k-\ell-1}}{(k-\ell-1)!}\*{{}_{2}F_{1}}\left(\ell+1-k,\ell+1-\mathrm{i}\eta;2\ell+2;2\right).}}$

Symbols List

• ${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: = F ( a , b ; c ; z ) notation for Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle\eta}}$: real parameter
• ${\displaystyle{\displaystyle A_{\ell+1}^{\ell}}}$: coefficient
 

Resources that cite this formula

No records found.