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Dual Hahn polynomials : ウィキペディア英語版
Dual Hahn polynomials
In mathematics, the dual Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined in terms of generalized hypergeometric functions by
:R_n(\lambda(x);\gamma,\delta,N)= {}_3F_2(-n,-x,x+\gamma+\delta+1;\gamma+1,-N;1).\ for 0≤''n''≤''N''
where λ(''x'')=''x''(''x''+γ+δ+1).
give a detailed list of their properties.
Closely related polynomials include the Hahn polynomials, the continuous Hahn polynomials ''p''''n''(''x'',''a'',''b'', , ), and the continuous dual Hahn polynomials ''S''''n''(''x'';''a'',''b'',''c''). These polynomials all have ''q''-analogs with an extra parameter ''q'', such as the q-Hahn polynomials ''Q''''n''(''x'';α,β, ''N'';''q''), and so on.
==Orthogonality==


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