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Review: A. H. Heatley, Some Integrals, Differential Equations and Series Related to the Modified Bessel Function of the First Kind

, 1940
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Geometric Properties of the Products of Modified Bessel Functions of the First Kind

Bulletin of the Malaysian Mathematical Sciences Society, 2021
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Khaled Mehrez, Sourav Das, Anish Kumar
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(p, q)-Extended Bessel and Modified Bessel Functions of the First Kind

Results in Mathematics, 2017
Inspired by certain recent extensions of the Euler's beta, Gauss hypergeometric and confluent hypergeometric functions [1], we introduce (p, q)- extended Bessel function J_{; ; ; \nu, p, q}; ; ; , the (p, q)- extended modified Bessel function I_{; ; ; ; \nu, p, q}; ; ; ; of the first kind of order \nu by making use two additional parameters in the ...
Jankov Maširević, Dragana, Parmar, Rakesh K., Pogány, Tibor K.   +2 more
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Multiple Orthogonal Polynomials Associated with the Modified Bessel Functions of the First Kind

Constructive Approximation, 2003
In the theory of orthogonality the connection between sequences of orthogonal polynomials (OPS) and the Padé table of rational approximation to a (formal) power series is well known. Already in the days of Ch. Hermite two different types of simultaneous rational `approximation' was known (in connection with transcendence proofs).
Coussement, Els, Van Assche, Walter
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Redheffer type bounds for Bessel and modified Bessel functions of the first kind

2017
In this paper our aim is to show some new inequalities of Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series.
Baricz, ��rp��d, Mehrez, Khaled
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On a second type Neumann series of modified Bessel functions of the first kind

Integral Transforms and Special Functions, 2020
The main aim of this article is to establish a summation formula for the second type Neumann series which members contain a product of two modified Bessel functions of the first kind of not necessarily equal orders and arguments.
Dragana Jankov Maširević, Tibor K. Pogány   +1 more
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Inequalities for the modified Bessel function of first kind of non-negative order

Journal of Mathematical Analysis and Applications, 2023
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Accurate solution for the modified Bessel function of the first kind

Advances in Engineering Software, 1995
Modelling of stochastic noise processes and physical systems frequently require the determination of the modified Bessel function of the first kind for positive integer orders. Precise and efficient evaluation of this function is described. Orders zero and one are solved over a wide range of argument using a convergent power and asymptotic series ...
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Convexity and concavity of the modified Bessel functions of the first kind with respect to Hölder means

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020
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Tie-Hong Zhao, Lei Shi, Yu-Ming Chu
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