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.
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| - Hahn-Polynom (de)
- Hahn polynomials (en)
- ハーン多項式 (ja)
- Hahnpolynom (sv)
- 哈恩多项式 (zh)
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| - Die Hahn-Polynome sind eine Menge orthogonaler Polynome im . Sie wurden 1875 von Tschebyscheff eingeführt und 1949 von Wolfgang Hahn wiederentdeckt. (de)
- ハーン多項式（はーんたこうしき、英語: Hahn polynomials）は直交多項式のひとつで、アスキースキームによって体系付けられる。 (ja)
- Inom matematiken är Hahnpolynomen en familj ortogonala polynom, introducerade av Pafnutij Tjebysjov 1875. upptäckte dem på nytt 1949. De definieras med hjälp av generaliserade hypergeometriska funktionen som (sv)
- 哈恩多项式是一个以德国数学家Wolfgang Hahn命名的正交多项式，由下列广义超几何函数定义： 前几个哈恩多项式为 (zh)
- 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. (en)
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| - Peter A. (en)
- René F. (en)
- Roderick S. C. (en)
- Roelof (en)
- Tom H. (en)
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| - Wong (en)
- Koekoek (en)
- Koornwinder (en)
- Lesky (en)
- Swarttouw (en)
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| - Springer Monographs in Mathematics (en)
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| - Hypergeometric orthogonal polynomials and their q-analogues (en)
- Hahn Class: Definitions (en)
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| - Die Hahn-Polynome sind eine Menge orthogonaler Polynome im . Sie wurden 1875 von Tschebyscheff eingeführt und 1949 von Wolfgang Hahn wiederentdeckt. (de)
- 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 Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw give a detailed list of their properties. If , these polynomials are identical to the discrete Chebyshev polynomials except for a scale factor. Closely related polynomials include the dual Hahn polynomials Rn(x;γ,δ,N), the continuous Hahn polynomials pn(x,a,b, a, b), and the continuous dual Hahn polynomials Sn(x;a,b,c). These polynomials all have q-analogs with an extra parameter q, such as the q-Hahn polynomials Qn(x;α,β, N;q), and so on. (en)
- ハーン多項式（はーんたこうしき、英語: Hahn polynomials）は直交多項式のひとつで、アスキースキームによって体系付けられる。 (ja)
- Inom matematiken är Hahnpolynomen en familj ortogonala polynom, introducerade av Pafnutij Tjebysjov 1875. upptäckte dem på nytt 1949. De definieras med hjälp av generaliserade hypergeometriska funktionen som (sv)
- 哈恩多项式是一个以德国数学家Wolfgang Hahn命名的正交多项式，由下列广义超几何函数定义： 前几个哈恩多项式为 (zh)
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