Results 201 to 210 of about 28,297 (240)

The exceptional Bessel polynomials

Integral Transforms and Special Functions, 2014
Gomez-Ullate, Kamran and Milson have found polynomial eigenfunctions of a Sturm–Liouville problem. These polynomials, denoted by X1-Laguerre and X1-Jacobi and starting with degree one, are eigenfunctions of a second-order linear differential operator. In this paper, we investigate the X1-Bessel case which we denote by .
M.J. Atia, S. Chneguir
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The Bessel Polynomials

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
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Filters using Bessel-type polynomials

IEEE Transactions on Circuits and Systems, 1976
Bessel-type polynomials are defined and shown to be useful in constructing a variety of transfer functions in filter theory. A generalized Bessel filter and a generalized Bessel rational filter are considered and shown to include a number of special cases of Bessel-type filters.
Johnson, Johnny R., Johnson, David E., Boudra, Paul W. jun., Stokes, Virgil P.   +3 more
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Asymptotic Series for Bessel Polynomials

Mathematical Notes, 2005
The ``squeezed'' Bessel polynomials \(B_{n}^{*}(z)\) which are defined by: \(B_{n}^{*}(z):=B_{n}(z/(an))\), \(a\in R\), \(a\neq 0\) where \(B_{n}(z)\) are the Bessel polynomials, are orthogonal with respect to a complex variable weight. In this paper the main result is a theorem describing the complete asymptotic expansion in powers of \(1/n\) for the ...
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The Basic Bessel Functions and Polynomials

SIAM Journal on Mathematical Analysis, 1981
Basic analogues of the Bessel polynomials and their generalization are introduced. These polynomials are orthogonal on the unit circle $| z | = 1$ with respect to a complex weight function. They satisfy a three-term recurrence relation, and the associated continued fraction is computed.
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The relativistic Bessel polynomials

1997
Summary: A new polynomial system of hypergeometric type is defined by means of the relativistic Laguerre polynomial system \(\big\{L_n^{(\alpha,N)}(x)\big\}_{n=0}^\infty\). These polynomials, denoted by \(\big\{y_n^{(N)}(x;a,b)\big\}_{n=0}^\infty\), are called relativistic generalized Bessel polynomials because they reduce, in the non-relativistic ...
NATALINI P., NOSCHESE, Silvia
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Remarks on the Bessel Polynomials

The American Mathematical Monthly, 1973
(1973). Remarks on the Bessel Polynomials. The American Mathematical Monthly: Vol. 80, No. 9, pp. 1034-1040.
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The irreducibility of the Bessel polynomials

Journal für die reine und angewandte Mathematik (Crelles Journal), 2002
\textit{E. Grosswald} in his book ``Bessel polynomials'' [Lect. Notes Math. 698, Springer (1978; Zbl 0416.33008)] conjectured that the \(n\)-th Bessel polynomial \(y_n(x)\) is irreducible over the rationals for every positive integer \(n\). The first author in an earlier paper [J. Number Theory 27, 22-32 (1987; Zbl 0624.33007)] proved that almost all \(
Filaseta, Michael, Trifonov, Ognian
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Generalized bessel functions and hermite polynomial

Il Nuovo Cimento B, 1993
After having recalled some essential definitions concerning the Generalized Bessel Functions (GBF) and the Modified Generalized Bessel Functions (MGBF), their proper terms according to the Hermite Polynomials will be found here, limited to the case of two variables and integer order.
B. Léauté, G. Marcilhacy, T. Melliti
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Generating Functions for Bessel and Related Polynomials

Canadian Journal of Mathematics, 1953
Krall and Frink [4] aroused interest in what they term Bessel polynomials.
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