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On polynomials connected to powers of Bessel functions [PDF]
International Journal of Number Theory, 2014 The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include recurrences in terms of
Victor H. Moll, Christophe Vignat
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Approximate Closed-Form Formulas for the Zeros of the Bessel Polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 We find approximate expressions x̃(k,n,a) and ỹ(k,n,a) for the real and imaginary parts of the kth zero zk=xk+iyk of the Bessel polynomial yn(x;a).
Rafael G. Campos, Marisol L. Calderón
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Canadian Journal of Mathematics, 1951 1. Krall and Frink [2] have recently considered in connection with certain solutions of the wave equation a system of polynomials yn(x), {n = 0, 1, 2, …), where yn is defined as that polynomial solution of the differential equation
J. L. Burchnall
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Multivariable Bessel polynomials related to the hyperbolic Sutherland model with external Morse potential [PDF]
, 2008 A multivariable generalisation of the Bessel polynomials is introduced and studied. In particular, we deduce their series expansion in Jack polynomials, a limit transition from multivariable Jacobi polynomials, a sequence of algebraically independent ...
Martin Hallnäs
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Computation of Fourier transform representations involving the generalized Bessel matrix polynomials [PDF]
Advances in Difference Equations, 2021 Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive the formulas for Fourier cosine and sine transforms of ...
M. Abdalla, M. Akel
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Note on the Bessel polynomials [PDF]
Transactions of the American Mathematical Society, 1954 1. This note can be considered as an addendum to the comprehensive study of the class of Bessel polynomials carried on by H. L. Krall and 0. Frink [1]. In fact I study here the expansion of particular functions in terms of Bessel polynomials as well as the location of the zeros of these polynomials. Write pn(z) = Zk PflkZk, so that [1, p. 101 ] (1) pnk
M. Nassif
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A Determinant Expression for the Generalized Bessel Polynomials [PDF]
Journal of Applied Mathematics, 2013 Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented
Sheng-liang Yang, Sai-nan Zheng
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Boletim da Sociedade Paranaense de Matemática, 2020 In the paper, by virtue of the Fa\'a di Bruno formula and identities for the Bell polynomials of the second kind, the author simplifies coefficients in a family of ordinary differential equations related to generating functions of reverse Bessel and ...
Feng Qi
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Canadian Journal of Mathematics, 1954 Recently a number of papers have been written on Bessel polynomials which arise as the solutions of the classical wave equation in spherical coordinates. Krall and Frink (5) studied in some detail the properties of these polynomials yn(x, a, b) defined as(1) .
Rajani Agarwal
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Linearization coefficients of Bessel polynomials
, 2005 We prove positivity results about linearization and connection coefficients for Bessel polynomials. The proof is based on a recursion formula and explicit formulas for the coefficients in special cases. The result implies that the distribution of a convex combination of independent Student-t random variables with arbitrary odd degrees of freedom has a ...
Christian Berg, Christophe Vignat
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