A new characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind
Copyright policy )A new characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind
We show that the only polynomial sets with a generating function of the form F (xt -- R(t)) and satisfying a three-term recursion relation are the monomial set and the rescaled ultraspherical, Hermite, and Chebyshev polynomials of the first kind.
- Université Mustapha Stambouli de Mascara Algeria
- University of Abou Bekr Belkaïd Algeria
- UNIVERSITE DE MASCARA Algeria
- Université de Tlemcen Algeria
Hermite polynomials, recurrence relations, Orthogonal polynomials, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], ultraspherical polynomials, Mathematics - Classical Analysis and ODEs, generating functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Chebyshev polynomials, orthogonal polynomials
Hermite polynomials, recurrence relations, Orthogonal polynomials, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], ultraspherical polynomials, Mathematics - Classical Analysis and ODEs, generating functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Chebyshev polynomials, orthogonal polynomials
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