Formula:6543

Digital Library of Mathematical Functions ID 18.20.E5

${\displaystyle{\displaystyle Q_{n}\left(x;\alpha,\beta,N\right)={{}_{3}F_{2}}\left({-n,n+\alpha+\beta+1,-x\atop\alpha+1,-N};1\right),}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$: alternatively F q p ( a ; b ; z ) or F q p ( a b ; z ) generalized hypergeometric function
• ${\displaystyle{\displaystyle Q_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{\beta},\NVar{N}\right)}}$: Hahn polynomial
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle N}}$: positive integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

Resources that cite this formula

No records found.