Results 71 to 80 of about 31,835 (251)
MathematicsThe objective of this paper is to investigate Hermite-based Peters-type Simsek polynomials with generating functions. By using generating function methods, we determine some of the properties of these polynomials.
Eda Yuluklu
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A model for the continuous q-ultraspherical polynomials
, 1995 We provide an algebraic interpretation for two classes of continuous $q$-polynomials. Rogers' continuous $q$-Hermite polynomials and continuous $q$-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the $q ...
Askey R. A. +4 more
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Structured Light Fields with 2D Tunable Indices Generated in a Raman Microchip Laser
Advanced Physics Research, EarlyView.HGm,n modes with 2D tunable indices of m up to 14 and n up to 2 oscillated in a highly efficient Yb:YAG/YVO4 Raman microchip laser pumped with a rectangular beam with a suitable ratio of wx/wy. Highâorder LGp,l optical vortices with 2D tunable radial index p up to 2, and azimuthal index up to 14 are converted with an astigmatic mode convertor ...
Ye Zhang +5 more
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An extension of Hermite polynomials [PDF]
International Journal of Contemporary Mathematical Sciences, 2014 In this paper, we introduce an extended Hermite polynomial ( , ) ( ) a b n H x , we establish its different forms, generating functions, basic recurrence relations, the pure recurrence relation, the second order differential equation, Rodrigues formula and orthogonality of the extended polynomial.
Ghulam Farid, G. M. Habibullah
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Context-Free Grammars for Several Triangular Arrays
Axioms, 2022 In this paper, we present a unified grammatical interpretation of the numbers that satisfy a kind of four-term recurrence relation, including the Bell triangle, the coefficients of modified Hermite polynomials, and the Bessel polynomials.
Roberta Rui Zhou, Jean Yeh, Fuquan Ren
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Finding identities and q-difference equations for new classes of bivariate q-matrix polynomials
Applied Mathematics in Science and EngineeringThis article introduces 2-variable q-Hermite matrix polynomials and delves into their complex representation, unravelling specific outcomes. The exploration encompasses the derivation of insightful identities for the q-cosine and q-sine analogues of the ...
Subuhi Khan, Hassan Ali, Mohammed Fadel
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Certain properties and characterizations of a novel family of bivariate 2D-q Hermite polynomials
Open MathematicsThis 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 +2 more
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Finite sums and generalized forms of Bernoulli polynomials [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1999 We introduce new classes of Bernoulli polynomials, useful to evaluate partial sums of Hermite and Laguerre polynomials. We also comment on the possibility of extending the class of Bernoulli numbers itself, and indicate their importance in the derivation
G. Dattoli, S. Lorenzutta, C. Cesarano
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On 2-variable q-Hermite polynomials
AIMS Mathematics, 2021 The quantum calculus has emerged as a connection between mathematics and physics. It has wide applications, particularly in quantum mechanics, analytic number theory, combinatorial analysis, operation theory etc.
Nusrat Raza +3 more
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On the hermite matrix of a polynomial
Linear Algebra and its Applications, 1971 AbstractWe investigate the location of the eigenvalues of the Hermite matrix of a given complex polynomial, the question under what conditions a given polynomial and the characteristic polynomial of its Hermite matrix are identical, and the question under what conditions the Hermite matrix has only one distinct eigenvalue.
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