Results 61 to 70 of about 246 (165)
Quantum Extensions of Widder’s Formula via q‐Deformed Calculus
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.In this study, we rigorously established q‐Widder’s formula of first and second kind by employing the q‐integral within a quantum calculus framework. Our approach introduces a novel formulation of the inverse q‐Laplace transform, enabling simplified computation without relying on conventional complex integration methods.
S. S. Naina Mohammed +6 more
wiley +1 more source
Connection Problem for Sums of Finite Products of Legendre and Laguerre Polynomials [PDF]
, 2019 The purpose of this paper is to represent sums of finite products of Legendre and Laguerre polynomials in terms of several orthogonal polynomials. Indeed, by explicit computations we express each of them as linear combinations of Hermite, generalized ...
Dmitry V. Dolgy +3 more
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Bi‐Starlike Function of Complex Order Involving Rabotnov Function Associated With Telephone Numbers
Journal of Mathematics, Volume 2025, Issue 1, 2025.Telephone numbers defined through the recurrence relation Qn=Qn−1+n−1Qn−2 for n ≥ 2, with initial values of Q0=Q1=1. The study of such numbers has led to the establishment of various classes of analytic functions associated with them. In this paper, we establish two new subclasses of bi‐convex and bi‐starlike functions of complex order in the open unit
Sa’ud Al-Sa’di +3 more
wiley +1 more source
Linearly-invariant families and generalized Meixner–Pollaczek polynomials [PDF]
, 2015 The extremal functions \(f_0(z)\) realizing the maxima of some functionals (e.g. \(\max|a_3|\), and \(\max{arg f^{'}(z)}\)) within the so-called universal linearly invariant family \(U_\alpha\) (in the sense of Pommerenke [10]) have such a form that \(
Naraniecka, Iwona +2 more
core +2 more sources
Continuous −1$-1$ hypergeometric orthogonal polynomials
Studies in Applied Mathematics, Volume 153, Issue 3, October 2024.Abstract The study of −1$-1$ orthogonal polynomials viewed as q→−1$q\rightarrow -1$ limits of the q$q$‐orthogonal polynomials is pursued. This paper presents the continuous polynomials part of the −1$-1$ analog of the q$q$‐Askey scheme. A compendium of the properties of all the continuous −1$-1$ hypergeometric polynomials and their connections is ...
Jonathan Pelletier +2 more
wiley +1 more source
On a Class of Generalized Multivariate Hermite–Humbert Polynomials via Generalized Fibonacci Polynomials [PDF]
This paper offers a thorough examination of a unified class of Humbert’s polynomials in two variables, extending beyond well-known polynomial families such as Gegenbauer, Humbert, Legendre, Chebyshev, Pincherle, Horadam, Kinnsy, Horadam–Pethe,
Ketan Kotecha +6 more
core +1 more source
Chain sequences and symmetric generalized orthogonal polynomials [PDF]
, 2002 in this paper, we derive an explicit expression for the parameter sequences of a chain sequence in terms of the corresponding orthogonal polynomials and their associated polynomials.
Dimitrov, D.K. +6 more
core +1 more source
Some Generating Functions of Modified Gegenbauer Polynomials by Lie Algebraic Method
Mathematics and Statistics, 2014 In this paper we have obtained some novel generating functions of C + n n (x)-a modification of Gegenbauer polynomials, C n (x) by utilizing L. Wesiner's group-theoretic method. By giving suitable interpretations to both the index (n) and the parameter () of the polynomial under consideration, we obtain, in section 2, a set of infinitesimal operators ...
K.P. Samanta, B. C. Chandra, C.S. Bera
openaire +1 more source
Noise‐Tailored Constructions for Spin Wigner Function Kernels
Advanced Physics Research, Volume 3, Issue 6, June 2024.This work explores the parameterization of spin Wigner functions to efficiently represent the effects of probabilistic unitary noise on a quantum state. Block diagonalization of the noise operator algebra is used to reduce the required number of parameters while maintaining the Stratonovich–Weyl conditions for the representation.
Michael Hanks, Soovin Lee, M.S. Kim
wiley +1 more source
Characterizations of Orthogonal Generalized Gegenbauer-Humbert Polynomials and Orthogonal Sheffer-type Polynomials [PDF]
, 2011 We present characterizations of the orthogonal generalized Gegen-bauer-Humbert polynomial sequences and the orthogonal Sheffer-type polynomial sequences.
He, Tian-Xiao
core