Results 31 to 40 of about 1,259 (74)
Integral Representations of Functional Series with Members Containing Jacobi Polynomials [PDF]
, 2012 MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10In this article we establish a double definite integral representation, and two other indefinite integral expressions for a functional series and its derivative with members containing Jacobi ...
Jankov, Dragana, Pogany, Tibor K.
core
, 2012 We explain the use and set grounds about applicability of algebraic transformations of arithmetic hypergeometric series for proving Ramanujan's formulae for $1/\pi$ and their generalisations.Comment: 6 ...
Zudilin, Wadim
core +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The Y‐function has emerged as a significant tool in generalized fractional calculus due to its ability to unify and extend numerous classical special functions and hypergeometric‐type functions. Applying the Marichev–Saigo–Maeda fractional integration and differentiation operators of any complex order to the Y‐function, this study establishes four ...
Engdasew Birhane +2 more
wiley +1 more source
Generating new classes of orthogonal polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 643-656, 1996., 1994 Given a sequence of monic orthogonal polynomials (MOPS), {Pn}, with respect to a quasi‐definite linear functional u, we find necessary and sufficient conditions on the parameters an and bn for the sequence to be orthogonal. In particular, we can find explicitly the linear functional v such that the new sequence is the corresponding family of orthogonal
Amílcar Branquinho +1 more
wiley +1 more source
A generating function of the squares of Legendre polynomials
, 2012 We relate a one-parametric generating function for the squares of Legendre polynomials to an arithmetic hypergeometric series whose parametrisation by a level 7 modular function was recently given by Shaun Cooper. By using this modular parametrisation we
Zudilin, Wadim
core +1 more source
On the Generalized Class of Multivariable Humbert‐Type Polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The present paper deals with the class of multivariable Humbert polynomials having generalization of some well‐known polynomials like Gegenbauer, Legendre, Chebyshev, Gould, Sinha, Milovanović‐Djordjević, Horadam, Horadam‐Pethe, Pathan and Khan, a class of generalized Humbert polynomials in two variables etc.
B. B. Jaimini +4 more
wiley +1 more source
New generating functions for multivariate biorthogonal polynomials on the N‐sphere
International Journal of Stochastic Analysis, Volume 8, Issue 1, Page 85-90, 1995., 1994 Certain multivariate biorthogonal polynomials on the N‐sphere arise in connection with quantum chromodynamics. These functions can be expressed in terms of Lauricella functions of the first kind, and multi‐dimensional generating functions for them are deduced by means of an extension of Bailey′s theorem.
Harold Exton
wiley +1 more source
On Laguerre-Sobolev matrix orthogonal polynomials
Open MathematicsIn this manuscript, we study some algebraic and differential properties of matrix orthogonal polynomials with respect to the Laguerre-Sobolev right sesquilinear form defined by ⟨p,q⟩S≔∫0∞p*(x)WLA(x)q(x)dx+M∫0∞(p′(x))*W(x)q′(x)dx,{\langle p,q\rangle }_ ...
Fuentes Edinson +2 more
doaj +1 more source
Umbral Methods and Harmonic Numbers
Axioms, 2018 The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Giuseppe Dattoli +3 more
doaj +1 more source
Some extensions of Bateman′s product formulas for the Jacobi polynomials
International Journal of Stochastic Analysis, Volume 8, Issue 4, Page 423-428, 1995., 1995 The authors derive generalizations of some remarkable product formulas of Harry Bateman (1882‐1946) for the classical Jacobi polynomials. They also show how the results considered here would lead to various families of linear, bilinear, and bilateral generating functions for the Jacobi and related polynomials.
Ming-Po Chen, H. M. Srivastava
wiley +1 more source