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Racah Polynomial

A hypergeometric class of orthogonal polynomials defined by

R_n(lambda(x);alpha,beta,gamma,delta) =_4F_3(-n,n+alpha+beta+1,-x,x+gamma+delta+1; alpha+1,beta+delta+1,gamma+1;1)
(1)

for n=0, 1, ..., N, where _4F_3(a,b,c,d;e,f,g;x) is a generalized hypergeometric function,

lambda(x)=x(x+gamma+delta+1),
(2)

and one of the following holds

{alpha+1=-N; beta+delta+1=-N; gamma+1=-N,
(3)

with N a nonnegative integer.

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References

Koekoek, R. and Swarttouw, R. F. "Racah." §1.2 in The Askey-Scheme of Hypergeometric Orthogonal Polynomials and its q-Analogue. Delft, Netherlands: Technische Universiteit Delft, Faculty of Technical Mathematics and Informatics Report 98-17, pp. 26-29, 1998.

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Racah Polynomial

Cite this as:

Weisstein, Eric W. "Racah Polynomial." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RacahPolynomial.html

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