Results 41 to 50 of about 1,304 (66)

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

Lacunary generating functions of Hermite polynomials and symbolic methods [PDF]

, 2015
We employ an umbral formalism to reformulate the theory of Hermite polynomials and the derivation of the associated lacunary generating ...
D. Babusci, G. Dattoli, GERMANO, Bruna, MARTINELLI, Maria Renata, P. E. Ricci   +4 more
core  

Efficient scheme for a category of variable-order optimal control problems based on the sixth-kind Chebyshev polynomials

Demonstratio Mathematica
The main goal of the present study is to introduce an operational collocation scheme based on sixth-kind Chebyshev polynomials (SCPs) to solve a category of optimal control problems involving a variable-order dynamical system (VODS). To achieve this goal,
Sadri Khadijeh, Hosseini Kamyar, Salahshour Soheil, Baleanu Dumitru, Ahmadian Ali, Park Choonkil   +5 more
doaj   +1 more source

Generalized Chebyshev polynomials of the second kind

, 2015
We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis.
AlQudah, Mohammad A.
core   +1 more source

Bivariate q-Laguerre–Appell polynomials and their applications

Applied Mathematics in Science and Engineering
Recently, the monomiality principle has been extended to q-polynomials, namely, the q-monomiality principle of q-Appell polynomials has been considered.
Mohammed Fadel, Nusrat Raza, Ahmed Al-Gonah, Ugur Duran   +3 more
doaj   +1 more source

Remarks on orthogonal polynomials with respect to varying measures and related problems

, 1992
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 255-258, 1993.
Xin Li
wiley   +1 more source

Certain properties and characterizations of a novel family of bivariate 2D-q Hermite polynomials

Open Mathematics
This study presents a novel family of bivariate 2D-qq Hermite polynomials. We derive explicit forms and qq-partial differential equations and investigate numerical aspects associated with these polynomials.
Wani Shahid Ahmad, Zayed Mohra, Nahid Tabinda   +2 more
doaj   +1 more source

Eulerian polynomials as moments, via exponential Riordan arrays [PDF]

, 2011
Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the "descending power" Eulerian polynomials, and their once shifted sequence, are moment sequences for simple families of orthogonal polynomials, which we ...
Barry, Paul
core   +3 more sources

On the L 2 -norm of Gegenbauer polynomials. [PDF]

Math Sci (Karaj), 2022
Ferizović D.
europepmc   +1 more source

Heat kernels of the discrete Laguerre operators. [PDF]

Lett Math Phys, 2021
Kostenko A.
europepmc   +1 more source