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Variational calculus approach to Zernike polynomials with application to fluorescence correlation spectroscopy

Gligonov I, Enderlein J.
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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 ...
D. Jankov Maširević, R. K. Parmar, T. Pogány   +2 more
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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, Fisicas Y Naturales - Serie A: Matematicas, 2020
Tie-hong Zhao, Lei Shi, Y. Chu
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Monotonicity of Three Classes of Functions Involving Modified Bessel Functions of the Second Kind

Bulletin of the Iranian Mathematical Society, 2023
Zhongjian Mao, Jing-feng Tian
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Modified Bessel Functions

Classical Electrodynamics, 2019
J. Schwinger, L. DeRaad, K. Milton, W. Tsai   +3 more
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Modified $ q$-Bessel functions and $ q$-Macdonald functions

Sbornik: Mathematics, 1996
Summary: The \(q\)-analogues of modified Bessel functions and Macdonald functions are defined in this paper. As in the case of \(q\)-Bessel functions introduced by Jackson, there are two kinds of these functions. Like their classical prototypes, they arise in harmonic analysis on quantum symmetric spaces.
Ol'shanetskij, M. A., Rogov, V.-B. K.
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Classical Magnetism and an Integral Formula Involving Modified Bessel Functions

International journal of nonlinear sciences and numerical simulation, 2018
We study an integral expression that is encountered in some classical spin models of magnetism. The idea is to calculate the key integral that represents the building block for the expression of the partition function of these models.
O. Ciftja
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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
K. Mehrez, Sourav Das, Anish Kumar
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Monotonicity and inequalities involving the modified Bessel functions of the second kind

Journal of Mathematical Analysis and Applications, 2021
Zhen-Hang Yang, Y. Chu
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Modified Bessel function asymptotics via probability

Statistics & Probability Letters, 1987
Let the modified Bessel function be defined by \[ I_{\rho}(x)=\sum^{\infty}_{k=0}\frac{1}{k!}\frac{1}{\Gamma (k+\rho +1)}(x/2)^{2k+\rho}\quad for\quad \rho \geq -1\quad and\quad -\infty
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