Results 81 to 90 of about 28,297 (240)

Symbolic computation of Appell polynomials using Maple

Electronic Journal of Differential Equations, 2001
This work focuses on the symbolic computation of Appell polynomials using the computer algebra system Maple. After describing the traditional approach of constructing Appell polynomials, the paper examines the operator method of constructing the same ...
H. Alkahby, G. Ansong, P. Frempong-Mireku, A. Jalbout   +3 more
doaj  

A New Class of Integrals Connected with Polynomials and Extended Generalized Mittag-Leffler Function [PDF]

Sahand Communications in Mathematical Analysis
The aim of the present investigation is to deal with integrals, which are connected with the extended generalized Mittag-Leffler function, Jacobi polynomial, and Bessel-Maitland function.
Nirmal Kumar Jangid, Sunil Joshi, Ekta Mittal   +2 more
doaj   +1 more source

Characterization of Generalized Bessel Polynomials in Terms of Polynomial Inequalities

Journal of Mathematical Analysis and Applications, 1998
The authors prove two theorems, each of which characterizes the generalized Bessel polynomials \(y_n(x;\alpha,\beta)\) as the extremal polynomials in certain interesting inequalities of Markov type in an \(L^2\) norm. Their results are based upon an orthogonality property of the generalized Bessel polynomials, which was considered earlier by the ...
de Andrade, EXL, Dimitrov, D. K., Ranga, A. S.   +2 more
openaire   +2 more sources

Character sum, reciprocity, and Voronoi formula

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3797-3823, December 2025.
Abstract We prove a novel four‐variable character sum identity that serves as a twisted, non‐Archimedean analog of Weber's integrals for Bessel functions. Using this identity and ideas from Venkatesh's thesis, we provide a short spectral proof of the Voronoi formulae for classical modular forms with character twists.
Chung‐Hang Kwan, Wing Hong Leung
wiley   +1 more source

Poisson kernels of q$q$‐3D Hermite polynomials expansion for functions of several variables via generalized q$q$‐heat equations

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
wiley   +1 more source

Theory of multiindex multivariable Bessel functions and Hermite polynomials

Le Matematiche, 1997
We discuss the theory of multivariable multiindex Bessel functions (B.F.) and Hermite polynomials (H.P.) using the generating function method. We derive addition and multiplication theorems and discuss how generalized H.P.
G. Dattoli, S. Lorenzutta, G. Maino, A. Torre   +3 more
doaj  

The Hermite polynomials and the Bessel functions from a general point of view

International Journal of Mathematics and Mathematical Sciences, 2003
We introduce new families of Hermite polynomials and of Bessel functions from a point of view involving the use of nonexponential generating functions.
G. Dattoli, H. M. Srivastava, D. Sacchetti   +2 more
doaj   +1 more source

Calculator of some special mathematical functions [PDF]

Serbian Journal of Electrical Engineering
This paper presents the implementation of a calculator of certain special mathematical functions in the form of an efficient web application with a simple and intuitive GUI (graphical user interface).
Lazić Sara, Iričanin Bratislav
doaj   +1 more source

Inequalities Concerning Ultraspherical Polynomials and Bessel Functions [PDF]

Proceedings of the American Mathematical Society, 1950
Presented to the Society, September 7,1948; received by the editors December 28, 1948. 1 This paper was written at the Institute for Numerical Analysis of the National Bureau of Standards, with the financial support of the Office of Naval Research of the U. S. Navy Department. * G. Szego, On an inequality of P.
openaire   +1 more source

A certain class of q-Bessel polynomials

Mathematical and Computer Modelling, 1994
A \(q\)-extension of the familiar Bessel polynomials is considered here from the point of view of their associated \(q\)-differential equation. The orthogonality of these \(q\)-Bessel polynomials is discussed. Several remarks and observations, relevant to the present investigation, are also made.
Exton, H., Srivastava, H. M.
openaire   +1 more source