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In mathematics, the Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials, introduced by Pafnuty Chebyshev in 1875 and rediscovered by Wolfgang Hahn . The Hahn class is a name for special cases of Hahn polynomials, including Hahn polynomials, Meixner polynomials, Krawtchouk polynomials, and Charlier polynomials. Sometimes the Hahn class is taken to include limiting cases of these polynomials, in which case it also includes the classical orthogonal polynomials. Hahn polynomials are defined in terms of generalized hypergeometric functions by : give a detailed list of their properties. Closely related polynomials include the dual Hahn polynomials ''R''''n''(''x'';γ,δ,''N''), 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== : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hahn polynomials」の詳細全文を読む スポンサード リンク
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