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A note on a modified Bessel function integral [article]

R.B. Paris
2015 arXiv   pre-print
We investigate the integral ∫_0^∞^μt K_ν(z t) dt (z)>0, where K denotes the modified Bessel function, for non-negative integer values of the parameters μ and ν.  ...  When the integers are of different parity, closed-form expressions are obtained in terms of z^-1e^-z multiplied by a polynomial in z^-1 of degree dependent on the sign of μ-ν.  ...  The integral (1.1) can also be expressed in terms of a combination of three 1 F 2 (z 2 /4) generalised hypergeometric functions.  ... 
arXiv:1510.00192v2 fatcat:gqhwvfeacvftrbn6tiokhvfczy

A numerical integration formula based on the Bessel functions

Hidenori Ogata
2005 Publications of the Research Institute for Mathematical Sciences  
) is a function analytic on the real axis (−∞, +∞).  ...  We also apply the quadrature formula to the numerical integration of integral involving the Bessel function.  ...  We tried to extend Ooura and Mori's DE formula to a one for integrals of the Hankel transform type, that is, integrals of the form (1.4) ∞ 0 f (x)J ν (x)dx, where J ν (x) is the Bessel function of order  ... 
doi:10.2977/prims/1145474602 fatcat:su5qgusil5chplz4755pdckr4q

On an integral equation with a bessel function kernel

James A. Cochran
1988 Journal of Integral Equations and Applications  
The integral equation /*oo g{*)= / Jï(v)f(y)dy, x>o, Jo which arises in certain problems in stereology, is solved for a wide class of input functions g(x) using transform techniques.  ...  which followed application of the integral representation for the Bessel function cross-product.  ...  The squared Bessel function kernel and the appearance of the independent variable in (1.1) are a bit unusual.  ... 
doi:10.1216/jie-1988-1-1-167 fatcat:lo5itx33dnaalj5cp4hwzgt5ji

A note on Bessel function dual integral equation with weight function

B. N. Mandal
1988 International Journal of Mathematics and Mathematical Sciences  
An elementary procedure based on Sonine's integrals has been used to reduce dual integral equations with Bessel functions of different orders as kernels and an arbitrary weight function to a Fredholm integral  ...  The result obtained here encompasses many results concerning dual integral equations with Bessel functions as kernels known in the literature.  ...  In a recent paper Nasim [2] used the 'multiplying-factor method' based on Sonine's integrals to a class of dual integral equations with Bessel functions of same order ( ) as kernels to a Fredholm  ... 
doi:10.1155/s0161171288000651 fatcat:eer5zeumcbgupevmwl2lcxf27y

A zero-one law for integral functionals of the bessel process [chapter]

Xing-Xiong Xue
1990 Lecture notes in mathematics  
Schmidt for advancing a preprint of the article [3] , and to Professor M.Yor for his many helpful remarks on an earlier version of this paper.  ...  Karatzas for suggesting this topic and for his many comments on this paper. He is also grateful to Dr. W.  ...  A Zero-One Law for Integral Functionals of The Bessel Process* By Xing-Xiong Xue Department of Statistics, Columbia University, New York, N.Y.10027 Abstract.  ... 
doi:10.1007/bfb0083762 fatcat:rl7c5tgaqvfxxomwxvvnw272m4

On the generalization of a method for computing bessel function integrals

Bruno Gabutti
1980 Journal of Computational and Applied Mathematics  
We extend a method for the numerical evaluation of integrals involving Bessel functions (of the first kind) to cover integrals which involve product of Bessel functions.  ...  In a previous paper [1] we described a useful method for the evaluation of integrals of the form : OO  ...  We extend a method for the numerical evaluation of integrals involving Bessel functions (of the first kind) to cover integrals which involve product of Bessel functions.  ... 
doi:10.1016/0771-050x(80)90010-8 fatcat:44etcroiing5nf5ho5wezqevzy

On a General Method for Resolving Integrals of Multiple Spherical Bessel Functions Against Power Laws into Distributions [article]

Kiersten Meigs, Zachary Slepian
2021 arXiv   pre-print
We here present a method of performing integrals of products of spherical Bessel functions (SBFs) weighted by a power-law.  ...  We also here display a suitable base integral expression to which this operator can be applied for both even and odd cases.  ...  Kamalinejad, A. Krolewski, O.H.E. Philcox, M. Simonovic, and M. White for many useful conversations, and especially R.N. Cahn for much insight into singular sBF integrals over several years, and J.  ... 
arXiv:2112.07809v1 fatcat:xpqd5rksmjaf5biwlfkj3lmgs4

A Class of Integral Operators and Bessel Plancherel Transform on

M. Dziri
2012 Journal of Function Spaces and Applications  
Building on these results we obtain a new properties of certain well-known integral transforms associated with the eigenfunction of the Bessel differential operator defined on (0, ∞) by , .  ...  We also construct a class of integral operators which commute with Bessel Plancherel transform.  ...  In particular we construct a class of integral operators which commute with the Bessel Plancherel transform on L 2 α . Theorem 4.1.  ... 
doi:10.1155/2012/419578 fatcat:4jof7bb7zjda3eyhms36yppud4

A note on a generalisation of a definite integral involving the Bessel function of the first kind [article]

S A Dar, M Kamarujjama, R B Paris
2022 arXiv   pre-print
We consider a generalisation of a definite integral involving the Bessel function of the first kind.  ...  It is shown that this integral can be expressed in terms of the Fox-Wright function _pΨ_q(z) of one variable. Some consequences of this representation are explored by suitable choice of parameters.  ...  Evaluation of the definite integral F 1 (µ, ξ, a, ν, y) In this section, we evaluate the integral in (1.11) involving the Bessel function of the first kind in terms of the Fox-Wright function.  ... 
arXiv:2205.03161v1 fatcat:zsro5j7dlbdcdfhp72kzbh7hum

On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials

Stamatis Koumandos
2007 International Journal of Mathematics and Mathematical Sciences  
In particular, we give a short proof of a recent result of A. A. R. Neves et al. regarding the analytical evaluation of an integral of a Bessel function times associated Legendre functions.  ...  We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer.  ...  A proof of (1.4) is given in [3, pages 378-379], using a method which is based on integration over a unit sphere.  ... 
doi:10.1155/2007/73750 fatcat:ogqcpn3kavd3pko7yjkziitvvq

A SURVEY ON BESSEL TYPE FUNCTIONS AS MULTI-INDEX MITTAG-LEFFLER FUNCTIONS: DIFFERENTIAL AND INTEGRAL RELATIONS

J. Paneva-Konovska
2019 International Journal of Applied Mathematics  
Wright firstly introduced them for µ > 0 and on a later stage, studying the asymptotic behavior of the Bessel-Maitland functions A SURVEY ON BESSEL TYPE FUNCTIONS AS... 359 for large values of |z|, he  ...  of indices, up to a matching power function.  ...  Projects 'Analytical and numerical methods for differential and integral equations and mathematical models of arbitrary (fractional or high integer) order' between BAS and SANU and 'Analysis, Geometry  ... 
doi:10.12732/ijam.v32i3.1 fatcat:q5hlh2txmfg7jekh57yvrqi3jm

On an integral of J-Bessel functions and its application to Mahler measure (with an appendix by J.S. Friedman*) [article]

George Anton, Jessen A. Malathu, Shelby Stinson
2021 arXiv   pre-print
We establish the case of 3 variables, by bounding an integral with integrand involving the random walk probability density a∫_0^∞ tJ_0(at) ∏_m=0^2 J_0(r_m t)dt, where J_0 is the order zero Bessel function  ...  of the first kind, and a and r_m are positive real numbers.  ...  is integrable on [0,1] we consider the integral on the interval [1, 8).  ... 
arXiv:2012.04165v3 fatcat:l6zi6mgi3zambpqgfvbp3cc5oi

A Note on the Graphs of the Bessel Functions of Integral Grder

B Hague
1916 Proceedings of the Physical Society of London  
In a recent investigation the writer had occasion to plot the graph of the function for certain integral values of n, and the t~e.julting curves seemed so interesting that a complete series of graphs was  ...  ues of the functions have been published from time to time. However, with the exception of J, and J,-the graphs of which are on Besscl Functions."MR. B.  ... 
doi:10.1088/1478-7814/29/1/319 fatcat:we62uzw55zbsjlujgvrip353ye

A note on the computation of integrals involving products of trigonometric and Bessel functions

Peter Linz, T. E. Kropp
1973 Mathematics of Computation  
A method useful in the numerical computation of integrals involving Bessel functions is extended to the case where the integrand contains products of trigonometric and Bessel functions.  ...  In a previous paper [1] , one of us presented a method suitable for the numerical computation of integrals of the form (1) Kp) = Í 1(x)Jo(Px)dx.  ...  and (3) B(p,t)= f 1(x)J0(px)J0(Tx)dx. 0 The method is based on the observation that the application of an Abel integral transform converts Bessel functions into trigonometric functions and thus integrals  ... 
doi:10.1090/s0025-5718-1973-0324878-7 fatcat:5luar47n3fbmpb6rlzq2rhxuwy

A Note on the Computation of Integrals Involving Products of Trigonometric and Bessel Functions

Peter Linz, T. E. Kropp
1973 Mathematics of Computation  
A method useful in the numerical computation of integrals involving Bessel functions is extended to the case where the integrand contains products of trigonometric and Bessel functions.  ...  . 0 The method is based on the observation that the application of an Abel integral transform converts Bessel functions into trigonometric functions and thus integrals involving Bessel functions into more  ...  In a previous paper [1] , one of us presented a method suitable for the numerical computation of integrals of the form (1) Kp) = Í 1(x)Jo(Px)dx.  ... 
doi:10.2307/2005522 fatcat:4ifcoj43mrdtdizfbnmzsw727i
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