Results 61 to 70 of about 320 (175)

Construction of the Shifted Modified Gegenbauer Polynomials and Approximation

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
This article is concerned with deriving a new system of orthogonal polynomials, derived from the Gegenbauer polynomials, modified by affine transforms in variable, named shifted Gegenbauer polynomials. They appear as solutions of linear differential equation.
Abdelhamid Rehouma, Hossein Jafari, Leopoldo Greco   +2 more
wiley   +1 more source

Old and New Identities for Bernoulli Polynomials via Fourier Series

International Journal of Mathematics and Mathematical Sciences, 2012
The Bernoulli polynomials Bk restricted to [0,1) and extended by periodicity have nth sine and cosine Fourier coefficients of the form Ck/nk. In general, the Fourier coefficients of any polynomial restricted to [0,1) are linear combinations of terms of ...
Luis M. Navas, Francisco J. Ruiz, Juan L. Varona   +2 more
doaj   +1 more source

Optimal Algebras and Novel Solutions of Time‐Fractional (2 + 1) − D European Call Option Model

Discrete Dynamics in Nature and Society, Volume 2025, Issue 1, 2025.
In this article, we analyse the time‐fractional (2 + 1) − D Black–Scholes model for European call options by employing Lie symmetry analysis. We derive the infinitesimal transformations and classify the optimal systems. Furthermore, under the geometric Brownian motion, we reduced the given model to ordinary differential equation (ODE) with integer ...
Gimnitz Simon S., B. Bira, Sathiyaraj Thambiayya, Palanivel M.   +3 more
wiley   +1 more source

On a Certain Class of Bi-Univalent Functions in Connection with Gegenbauer Polynomials

Pan-American Journal of Mathematics
Recent direction of studies shows that there is a kin connection between regular functions and orthogonal polynomials. In this paper, we study a new class of regular and bi-univalent functions that involve the familiar Gegenbauer polynomials.
Rasheed Olawale Ayinla, Ayotunde Olajide Lasode   +1 more
doaj   +1 more source

Certain Constraints for Functions Provided by Touchard Polynomials

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
Since finding solutions to integral equations is usually challenging analytically, approximate methods are often required, one of which is based on Touchard polynomials. This paper examines the necessary constraints for the functions Ϝετς,Πε,τ,ςℏ, and the integral operator Lετς, defined by Touchard polynomials, to be in the comprehensive subclass ∁η(q3,
Tariq Al-Hawary, Mohamed Illafe, Feras Yousef, Shikha Binwal   +3 more
wiley   +1 more source

Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials

Mathematics, 2019
The aim of this paper is to solve a class of non-linear fractional variational problems (NLFVPs) using the Ritz method and to perform a comparative study on the choice of different polynomials in the method.
Harendra Singh, Rajesh K. Pandey, Hari Mohan Srivastava   +2 more
doaj   +1 more source

Studies in Sums of Finite Products of the Second, Third, and Fourth Kind Chebyshev Polynomials

Mathematics, 2020
In this paper, we consider three sums of finite products of Chebyshev polynomials of two different kinds, namely sums of finite products of the second and third kind Chebyshev polynomials, those of the second and fourth kind Chebyshev polynomials, and ...
Taekyun Kim, Dae San Kim, Hyunseok Lee, Jongkyum Kwon   +3 more
doaj   +1 more source

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, K. Jeevanandham, A. Ramalingam, R. Maheswari, Prasantha Bharathi Dhandapani, Rebecca Muhumuza Nalule, Kaviarasan Boomipalagan   +6 more
wiley   +1 more source

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, Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Ming-Sheng Liu   +3 more
wiley   +1 more source

The Numerical Approximation of Caputo Fractional Derivatives of Higher Orders Using a Shifted Gegenbauer Pseudospectral Method: A Case Study of Two-Point Boundary Value Problems of the Bagley–Torvik Type

Mathematics
This paper introduces a novel Shifted Gegenbauer Pseudospectral (SGPS) method for approximating Caputo fractional derivatives (FDs) of an arbitrary positive order.
Kareem T. Elgindy
doaj   +1 more source