On a generalization of the generating function for Gegenbauer polynomials [PDF]
Integral Transforms and Special Functions, 2013 A generalization of the generating function for Gegenbauer polynomials is introduced whose coefficients are given in terms of associated Legendre functions of the second kind. We discuss how our expansion represents a generalization of several previously derived formulae such as Heine's formula and Heine's reciprocal square-root identity.
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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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One-Step Recurrences for Stationary Random Fields on the Sphere [PDF]
, 2016 Recurrences for positive definite functions in terms of the space dimension have been used in several fields of applications. Such recurrences typically relate to properties of the system of special functions characterizing the geometry of the underlying
Beatson, R. K., Castell, W. zu
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Fekete-Szegö Functional for Bi-univalent Functions Related with Gegenbauer Polynomials
Journal of Mathematics, 2022 In this paper, we introduce and investigate a new subclass of bi-univalent functions related with generating function of Gegenbauer polynomials. We will mainly find bounds on Maclaurin series coefficients for functions belonging to this class.
Ibrar Ahmad +4 more
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On the local time of random walks associated with Gegenbauer polynomials
, 2010 The local time of random walks associated with Gegenbauer polynomials $P_n^{(\alpha)}(x),\ x\in [-1,1]$ is studied in the recurrent case: $\alpha\in\ [-\frac{1}{2},0]$.
Guillotin-Plantard, Nadine
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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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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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New connection formulae for the q-orthogonal polynomials via a series expansion of the q-exponential
, 2006 Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and q-Gegenbauer ...
Aizawa N Chakrabarti R Naina Mohammed S S Segar J +9 more
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Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon [PDF]
, 2010 We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis.
Adcock, Ben, Hansen, Anders C.
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The affine group and generalized Gegenbauer polynomials
Computers & Mathematics with Applications, 2001 AbstractOperators of the form f(xD) — g(L), where L is a shift (lowering) operator, arise naturally in the study of stochastic processes, such as Brownian motion, on the affine group. We find the polynomial eigenfunctions and the action of the affine group as well as the matrix elements of an exponential function corresponding to L.
Ph. Feinsilver, Uwe Franz
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