Results 11 to 20 of about 27,421 (244)
Densely generated 2D q-Appell polynomials of Bessel type and q-addition formulas
Boletim da Sociedade Paranaense de Matemática, 2022 The article aims to introduce a densely generated class of $2D$ $q$-Appell polynomials of Bessel type via generating equation and to establish its $q$-determinant form. It is advantageous to consider the $2D$ $q$-Bernoulli, $2D$ $q$-Roger Szeg\"{o} and $
Mumtaz Riyasat
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Acta Polytechnica, 2022 The paper advances Odake and Sasaki’s idea to re-write eigenfunctions of rationally deformed Morse potentials in terms of Wronskians of Laguerre polynomials in the reciprocal argument. It is shown that the constructed quasi-rational seed solutions of the
Gregory Natanson
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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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New analytic results for the Zernike circle polynomials from a basic result in the Nijboer-Zernike diffraction theory [PDF]
Journal of the European Optical Society-Rapid Publications, 2011 Several quantities related to the Zernike circle polynomials admit an expression, via the basic identity in the diffraction theory of Nijboer and Zernike, as an infinite integral involving the product of two or three Bessel functions. In this paper these
Janssen A. J. E. M.
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On Hankel transforms of generalized Bessel matrix polynomials
AIMS Mathematics, 2021 The present article deals with the evaluation of the Hankel transforms involving Bessel matrix functions in the kernel. Moreover, these transforms are associated with products of certain elementary functions and generalized Bessel matrix polynomials.
Mohamed Abdalla
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Certain integrals involving generalized Mittag-Leffler type functions
Vojnotehnički Glasnik, 2022 Introduction/purpose: Certain integrals involving the generalized MittagLeffler function with different types of polynomials are established. Methods: The properties of the generalized Mittag-Leffler function are used in conjunction with different ...
Sirazul Haq +3 more
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Recurrence Relations for Strongly q-Log-Convex Polynomials [PDF]
, 2008 We consider a class of strongly q-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanujan polynomials and the Dowling polynomials are strongly
Arthur L. B. Yang +6 more
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A Unified Approach to Computing the Zeros of Orthogonal Polynomials
Journal of New Theory, 2023 We present a unified approach to calculating the zeros of the classical orthogonal polynomials and discuss the electrostatic interpretation and its connection to the energy minimization problem. This approach works for the generalized Bessel polynomials,
Ridha Moussa, James Tipton
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A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type [PDF]
, 2009 In this paper we consider a large class of many-variable polynomials which contains generalisations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the eigenfunctions of ...
Hallnäs, Martin, Langmann, Edwin
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Appell-Type Functions and Chebyshev Polynomials
Mathematics, 2019 In a recent article we noted that the first and second kind Cebyshev polynomials can be used to separate the real from the imaginary part of the Appell polynomials. The purpose of this article is to show that the same classic polynomials can also be used
Pierpaolo Natalini, Paolo Emilio Ricci
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