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Some Generating Functions for the Generalized Bessel Polynomials
Studies in Applied Mathematics, 1992The authors begin by presenting a systematic (historical) account of some linear generating functions for the generalized Bessel polynomials. It is then shown how these linear generating functions can be applied with a view to obtaining various new families of bilinear, bilateral, or mixed multilateral generating functions for the generalized Bessel ...
Chen, Ming-Po +2 more
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Generalized Bessel Functions and Lie Algebra Representation
Mathematical Physics, Analysis and Geometry, 2005The authors derive generating relations involving generalized Bessel functions using the representation theory of the Lie group \(T_{3}\). The 2-index 3-variable 1-parameter Bessel functions (2I3V1PBF) \(J_{n,m}(x,\,y,\,z;\,\xi)\) can be defined by \[ J_{m,n}(x,\,y,\,z;\,\xi)=\sum_{s=-\infty}^{\infty} \xi^sJ_{m-s}(x)\,J_{n-s}(y)\,J_{s}(z), \] where ...
Khan, Subuhi, Yasmin, Ghazala
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Generalized Bessel functions: Theory and their applications
Mathematical Methods in the Applied Sciences, 2017This paper presents 2 new classes of the Bessel functions on a compact domain [0,T] as generalized‐tempered Bessel functions of the first‐ and second‐kind which are denoted by GTBFs‐1 and GTBFs‐2. Two special cases corresponding to the GTBFs‐1 and GTBFs‐2 are considered.
Hassan Khosravian‐Arab +2 more
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Geometric Properties of Generalized Bessel Functions
Publicationes Mathematicae Debrecen, 2008Summary: Our aim is to establish some geometric properties (like univalence, starlikeness, convexity and close-to-convexity) for the generalized Bessel functions of the first kind. In order to prove our main results, we use the technique of differential subordinations developed by \textit{S. S. Miller and P. T. Mocanu} [J. Differ.
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Lie-theoretic generating functions of multivariable generalized Bessel functions
Reports on Mathematical Physics, 1997Here the authors obtain generating functions for the one-parameter generalized Bessel function \(J_n (x,y;s)\) by using the representation of the Lie group \(T_3\). A few special cases of the above Bessel function are also discussed.
Pathan, M. A. +2 more
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Generalized bessel functions and hermite polynomial
Il Nuovo Cimento B, 1993After 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, 1953Krall and Frink [4] aroused interest in what they term Bessel polynomials.
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Generating functions of multivariable generalized Bessel functions and Jacobi-elliptic functions
Journal of Mathematical Physics, 1992It is pointed out that the Jacobi-elliptic functions are the natural basis to get generating functions of the multivariable generalized Bessel functions. Analytical and numerical results are given of interest for applications.
Dattoli, G +5 more
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Generalized Bessel Functions for p-Radial Functions
Constructive Approximation, 2007Suppose that \(d\in{\Bbb N}\) and p > 0. In this paper we study the generalized Bessel functions for the surface \(\{{\bf v}\in{\Bbb R}^d:|{\bf v}|_p=1\}\), introduced by D.St.P. Richards. We derive a recurrence relation for these functions and utilize a series representation to relate them to the classical symmetric functions. These generalized Bessel
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Lemniscate convexity of generalized Bessel functions
Studia Scientiarum Mathematicarum Hungarica, 2019Abstract Sufficient conditions on associated parameters p, b and c are obtained so that the generalized and “normalized” Bessel function up(z) = up,b,c(z) satisfies the inequalities ∣(1 + (zu″p(z)/u′p(z)))2 − 1∣ < 1 or ∣((zup(z))′/up(z))2 − 1∣ < 1. We also determine the condition on these parameters so that . Relations between the
Vibha Madaan +2 more
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