Results 71 to 80 of about 18,610 (207)

q-Calculus as operational algebra; pp. 73–97 [PDF]

Proceedings of the Estonian Academy of Sciences, 2009
This second paper on operational calculus is a continuation of Ernst, T. q-Analogues of some operational formulas. Algebras Groups Geom., 2006, 23(4), 354–374. We find multiple q-analogues of formulas in Carlitz, L.
Thomas Ernst
doaj   +1 more source

Relations for zeros of special polynomials associated to the Painleve equations

, 2006
A method for finding relations for the roots of polynomials is presented. Our approach allows us to get a number of relations for the zeros of the classical polynomials and for the roots of special polynomials associated with rational solutions of the ...
Ablowitz, Ahmed, Amdeberhan, Bassom, Calogero, Clarkson, Clarkson, Clarkson, Clarkson, Clarkson, Conte, Cosgrove, Demina, Demina, Hone, Iwasaki, Jrad, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Maria V. Demina, Mugan, Nikolai A. Kudryashov, Okamoto, Pickering, Stieltjes, Stieltjes, Szego, Umemura, Veselov, Vorob'ev, Yablonskii   +36 more
core   +1 more source

Performance Analysis of the LDPC‐Coded Hybrid LQAM‐MPPM for UWOC Systems

IET Optoelectronics, Volume 20, Issue 1, January/December 2026.
The effectiveness of LDPC codes in improving the performance of hybrid modulations is discussed, with coded 128‐QAM‐(12, 2) MPPM offering ~6.5 and 5.8 dB code gains at a BER of in strong and moderate turbulence, respectively. These results demonstrate the promise of hybrid modulation with LDPC as a robust and efficient modulation scheme for UWOC ...
Hongyan Jiang, Wanyi Hu, Xin Liao, Ning He, Wasiu Popoola, Ahmad Fairuz Omar, Sujan Rajbhandari   +6 more
wiley   +1 more source

DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER WITH ORTHOGONAL POLYNOMIAL SOLUTIONS

Pesquimat, 2014
In this paper we developed conditions for orthogonality of polynomial Solutions of the fourth order differential equations with polynomial coefficients.
Santiago César Rojas Romero
doaj   +1 more source

Approximation and Orthogonality on Fully Symmetric Domains

Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.
ABSTRACT We study orthogonal polynomials on a fully symmetric planar domain Ω$\Omega$ that is generated by a certain triangle in the first quadrant. For a family of weight functions on Ω$\Omega$, we show that orthogonal polynomials that are even in the second variable on Ω$\Omega$ can be identified with orthogonal polynomials on the unit disk composed ...
Yuan Xu
wiley   +1 more source

Extended forms of Legendre-Laguerre-based hybrid polynomials and their characteristics via fractional operator approach

Journal of Inequalities and Applications
This study presents an extensive generalization of Legendre–Laguerre polynomials along with their Appell-type counterparts. Using the quasi-monomiality approach, we establish core analytical features, including recurrence relations, associated ...
Waseem Ahmad Khan, Shahid Ahmad Wani, Mohammad Ayman-Mursaleen, Ketan Kotecha, Prakash Jadhav   +4 more
doaj   +1 more source

Asymptotic approximations to the nodes and weights of Gauss-Hermite and Gauss-Laguerre quadratures [PDF]

, 2017
Asymptotic approximations to the zeros of Hermite and Laguerre polynomials are given, together with methods for obtaining the coefficients in the expansions.
Gil, A., Segura, J., Temme, N. M.
core   +1 more source

Laguerre derivative and monogenic Laguerre polynomials: An operational approach

Mathematical and Computer Modelling, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cação, I., Falcão, M. I., Malonek, H. R.   +2 more
openaire   +4 more sources

A Review of Certain Modern Special Functions and Their Applications

Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.
This review article comprehensively analyzes recent developments in the generalization of special functions (SFs) and polynomials via various fractional calculus operators (FCOs), focusing on the analytical properties and applications of extended Hurwitz–Lerch zeta, Wright, and hypergeometric functions.
Hala Abd Elmageed, Mohamed Abdalla, AbdelMaksoud Soliman   +2 more
wiley   +1 more source

The Spectral Connection Matrix for Any Change of Basis within the Classical Real Orthogonal Polynomials

Mathematics, 2015
The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
doaj   +1 more source