Bounds and algorithms for the K-Bessel function of imaginary order [PDF]
, 2013 Using the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function of imaginary order and its first two derivatives with respect to the order.
Booker, Andrew R +5 more
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The method of finite-product extraction and an application to Wiener-Hopf theory [PDF]
, 2011 Copyright @ The Author, 2011. The publisher version of the article can be accessed at the link below.In this work we describe a simple method for finding approximate representations for special functions which are entire transcendental functions that can
Rawlins, AD, A. D. Rawlins
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Complete elliptic integrals resulting from infinite integrals of Bessel functions [PDF]
, 1974 Infinite integrals of Bessel and modified Bessel functions reducible to complete elliptic integrals are compiled.
Okui, Shigehiko
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An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments [PDF]
Advances in Computational Mathematics, 2017 We describe a method for the rapid numerical evaluation of the Bessel functions of the first and second kinds of nonnegative real orders and positive arguments.
J. Bremer
semanticscholar +1 more source
Asymptotic behavior and zero distribution of polynomials orthogonal with respect to Bessel functions [PDF]
, 2015 We consider polynomials P_n orthogonal with respect to the weight J_? on [0,?), where J_? is the Bessel function of order ?. Asheim and Huybrechs considered these polynomials in connection with complex Gaussian quadrature for oscillatory integrals.
Deaño Cabrera, Alfredo +5 more
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On Geometric Properties of Normalized Hyper-Bessel Functions
Mathematics, 2019 In this paper, the normalized hyper-Bessel functions are studied. Certain sufficient conditions are determined such that the hyper-Bessel functions are close-to-convex, starlike and convex in the open unit disc.
Khurshid Ahmad +5 more
doaj +1 more source
On spherical Bessel functions [PDF]
Transactions of the American Mathematical Society, 1965 In [1] solutions were obtained for certain second order linear differential equations with polynomial coefficients in terms of generalized Rodrigues' formulas and iterated indefinite integrals. The purpose of this paper is to apply these results to the Bessel equation.
openaire +2 more sources
Bessel Functions. (Scientific Books: A Treatise on the Theory of Bessel Functions)
, 1923 1. Bessel functions before 1826 2. The Bessel coefficients 3. Bessel functions 4. Differential equations 5. Miscellaneous properties of Bessel functions 6. Integral representations of Bessel functions 7.
G. Watson
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Fractional-order Bessel functions with various applications
Applied Mathematics, 2019 We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus.
Haniye Dehestani +2 more
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Theory of Fundamental Bessel Functions of High Rank [PDF]
Memoirs of the American Mathematical Society, 2016 In this article, we shall study fundamental Bessel functions for $\mathrm{GL}_n(\mathbb{F})$ arising from the Vorono\"i summation formula for any rank $n$ and field $\mathbb{F} = \mathbb{R}$ or $\mathbb{C}$, with focus on developing their analytic and ...
Zhi Qi
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