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A note on a modified Bessel function integral
[article]

2015
*
arXiv
*
pre-print

We investigate the

arXiv:1510.00192v2
fatcat:gqhwvfeacvftrbn6tiokhvfczy
*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*. ...##
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A numerical integration formula based on the Bessel functions

2005
*
Publications of the Research Institute for Mathematical Sciences
*

) is

doi:10.2977/prims/1145474602
fatcat:su5qgusil5chplz4755pdckr4q
*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 ...##
###
On an integral equation with a bessel function kernel

1988
*
Journal of Integral Equations and Applications
*

The

doi:10.1216/jie-1988-1-1-167
fatcat:lo5itx33dnaalj5cp4hwzgt5ji
*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. ...##
###
A note on Bessel function dual integral equation with weight function

1988
*
International Journal of Mathematics and Mathematical Sciences
*

An elementary procedure based

doi:10.1155/s0161171288000651
fatcat:eer5zeumcbgupevmwl2lcxf27y
*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 ...##
###
A zero-one law for integral functionals of the bessel process
[chapter]

1990
*
Lecture notes in mathematics
*

Schmidt for advancing

doi:10.1007/bfb0083762
fatcat:rl7c5tgaqvfxxomwxvvnw272m4
*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. ...##
###
On the generalization of a method for computing bessel function integrals

1980
*
Journal of Computational and Applied Mathematics
*

We extend

doi:10.1016/0771-050x(80)90010-8
fatcat:44etcroiing5nf5ho5wezqevzy
*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*. ...##
###
On a General Method for Resolving Integrals of Multiple Spherical Bessel Functions Against Power Laws into Distributions
[article]

2021
*
arXiv
*
pre-print

We here present

arXiv:2112.07809v1
fatcat:xpqd5rksmjaf5biwlfkj3lmgs4
*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. ...##
###
A Class of Integral Operators and Bessel Plancherel Transform on

2012
*
Journal of Function Spaces and Applications
*

Building

doi:10.1155/2012/419578
fatcat:4jof7bb7zjda3eyhms36yppud4
*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. ...##
###
A note on a generalisation of a definite integral involving the Bessel function of the first kind
[article]

2022
*
arXiv
*
pre-print

We consider

arXiv:2205.03161v1
fatcat:zsro5j7dlbdcdfhp72kzbh7hum
*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*. ...##
###
On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials

2007
*
International Journal of Mathematics and Mathematical Sciences
*

In particular, we give

doi:10.1155/2007/73750
fatcat:ogqcpn3kavd3pko7yjkziitvvq
*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. ...##
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A SURVEY ON BESSEL TYPE FUNCTIONS AS MULTI-INDEX MITTAG-LEFFLER FUNCTIONS: DIFFERENTIAL AND INTEGRAL RELATIONS

2019
*
International Journal of Applied Mathematics
*

Wright firstly introduced them for µ > 0 and

doi:10.12732/ijam.v32i3.1
fatcat:q5hlh2txmfg7jekh57yvrqi3jm
*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 ...##
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On an integral of J-Bessel functions and its application to Mahler measure (with an appendix by J.S. Friedman*)
[article]

2021
*
arXiv
*
pre-print

We establish the case of 3 variables, by bounding an

arXiv:2012.04165v3
fatcat:l6zi6mgi3zambpqgfvbp3cc5oi
*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). ...##
###
A Note on the Graphs of the Bessel Functions of Integral Grder

1916
*
Proceedings of the Physical Society of London
*

In

doi:10.1088/1478-7814/29/1/319
fatcat:we62uzw55zbsjlujgvrip353ye
*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. ...##
###
A note on the computation of integrals involving products of trigonometric and Bessel functions

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*...

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

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. ...

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