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Certain results on generating functions related to the associated Meixner-Pollaczek polynomials
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In this article, a new form of a generating function for the c-associated Meixner-Pollaczek polynomials was derived, which is of particular importance since its several r...Citations
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Some Families of Generating Functions Associated with Orthogonal Polynomials and Other Higher Transcendental Functions
TL;DR: In this article , the authors present a brief and comprehensive account of some general families of linear and bilinear generating functions which are associated with orthogonal polynomials and such other higher transcendental functions as (for example) hypergeometric functions in one, two and more variables.
On the spherical clothoid
TL;DR: In this article , the spherical clothoid is revisited as a nonlinear spline primitive for 3-space and its Cartesian coordinate functions using confluent hypergeometric functions (the Kummer functions) and its stereographic projection onto the complex plane.
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The Hahn and Meixner polynomials of an imaginary argument and some of their applications
TL;DR: In this article, the Hahn and Meixner polynomials of a discrete variable are analytically continued in the complex plane both in variable and parameter, leading to the origination of two systems of real polynomial systems orthogonal with respect to a continuous measure.
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Linear birth and death models and associated Laguerre and Meixner polynomials
TL;DR: In this paper, the authors studied birth and death processes with linear rates λ n = n+α + c + 1, μ n + 1 = n + c, n ⩾ 0 and μ 0 is either zero or c. The spectral measures of both processes were found using generating functions and the integral transforms of Laplace and Stieltjes.
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The lagrange polynomials in several variables
TL;DR: In this article, a multi-variable extension of the familiar Lagrange polynomials which are known to occur in certain problems in statistics is introduced and investigated, and the main object of this paper is to present various families of linear multilinear, and mixed multilateral generating functions.
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Some new results for the lagrange polynomials in several variables
TL;DR: In this article, Chan et al. derived some generalizations of this summation identity for the Chan-Chyan-Srivastava polynomials in several variables.
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Fourth-order difference equation for the associated Meixner and Charlier polynomials
TL;DR: An explicit representation of the associated Meixner polynomials (with a real association parameter γ ⩾0) is given in terms of hypergeometric functions.