Formula:6598

Digital Library of Mathematical Functions ID 18.23.E1

${\displaystyle{\displaystyle{{}_{1}F_{1}}\left({-x\atop\alpha+1};-z\right){{}_{1}F_{1}}\left({x-N\atop\beta+1};z\right)=\sum_{n=0}^{N}\frac{{\left(-N\right)_{n}}}{{\left(\beta+1\right)_{n}}n!}Q_{n}\left(x;\alpha,\beta,N\right)z^{n},}}$

Constraint(s)

${\displaystyle{\displaystyle x=0,1,\dots,N}}$

Symbols List

• ${\displaystyle{\displaystyle Q_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{\beta},\NVar{N}\right)}}$: Hahn polynomial
• ${\displaystyle{\displaystyle{{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)}}$: = M ( a , b , z ) notation for the Kummer confluent hypergeometric function
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle N}}$: positive integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

Resources that cite this formula

No records found.