Results 31 to 40 of about 696 (218)
Mathematics, 2018 This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim +3 more
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Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials
Mathematics, 2019 In the classical connection problem, it is dealt with determining the coefficients in the expansion of the product of two polynomials with regard to any given sequence of polynomials.
Dae San Kim +3 more
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Mathematics, 2015 The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
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Some identities involving Gegenbauer polynomials [PDF]
Advances in Difference Equations, 2012 11 ...
Kim, Dae, Kim, Taekyun, Rim, Seog-Hoon
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A Survey on Orthogonal Polynomials from a Monomiality Principle Point of View
EncyclopediaThis survey highlights the significant role of exponential operators and the monomiality principle in the theory of special polynomials. Using operational calculus formalism, we revisited classical and current results corresponding to a broad class of ...
Clemente Cesarano +2 more
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Generalized Mixed Type Bernoulli-Gegenbauer Polynomials
Kragujevac Journal of Mathematics, 2023 The generalized mixed type Bernoulli-Gegenbauer polynomials of order α >−1/2 are special polynomials obtained by use of the generating function method. These polynomials represent an interesting mixture between two classes of special functions, namely generalized Bernoulli polynomials and Gegenbauer polynomials.
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Reconstruction Techniques for Inverse Sturm–Liouville Problems With Complex Coefficients
Mathematical Methods in the Applied Sciences, Volume 48, Issue 17, Page 15875-15889, 30 November 2025.ABSTRACT A variety of inverse Sturm–Liouville problems is considered, including the two‐spectrum inverse problem, the problem of recovering the potential from the Weyl function, as well as the recovery from the spectral function. In all cases, the potential in the Sturm–Liouville equation is assumed to be complex valued.
Vladislav V. Kravchenko
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Coefficient Bounds for a Certain Family of Biunivalent Functions Defined by Gegenbauer Polynomials
Journal of Mathematics, 2022 In the present work, by making use of Gegenbauer polynomials, we introduce and study a certain family of λ-pseudo bistarlike and λ-pseudo biconvex functions with respect to symmetrical points defined in the open unit disk. We obtain estimates for initial
Isra Al-Shbeil +3 more
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 13, Page 12654-12674, September 2025.ABSTRACT We have studied possible applications of a particular pseudodifferential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The pseudodifferential algebra considered in the present work, comprises degenerate partial differential ...
Heinz‐Jürgen Flad +1 more
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On Generating Relations Involving Generalized Gegenbauer Polynomials [PDF]
Georgian Mathematical Journal, 2006 Abstract In this paper, generating relations involving generalized Gegenbauer polynomials are obtained by constructing a three-dimensional Lie algebra isomorphic to special linear algebra sl(2). Further, a number of new interesting relations involving various generalized polynomials are obtained as applications of these generating ...
Khan, Subuhi +2 more
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