Certain unified integrals involving a product of Bessel functions of the first kind (original) (raw)

Certain new unified integrals associated with the product of generalized Bessel functions

Communications in Numerical Analysis, 2016

Our focus to presenting two very general integral formulas whose integrands are the integrand given in the Oberhettingers integral formula and a finite product of the generalized Bessel function of the first kind, which are expressed in terms of the generalized Lauricella functions. Among a large number of interesting and potentially useful special cases of our main results, some integral formulas involving such elementary functions are also considered.

Certain New Integral Formulas Involving the Generalized Bessel Functions

Bulletin of the Korean Mathematical Society, 2014

A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas involving various Bessel functions have been presented. Very recently, Choi and Agarwal derived two generalized integral formulas associated with the Bessel function Jν (z) of the first kind, which are expressed in terms of the generalized (Wright) hypergeometric functions. In the present sequel to Choi and Agarwal's work, here, in this paper, we establish two new integral formulas involving the generalized Bessel functions, which are also expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

On a new class of integrals involving Bessel functions of the first kind

Communications in Numerical Analysis, 2014

In recent years, several integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas containing the Bessel function J ν (z) have been presented. Very recently, Rakha et al. presented some generalized integral formulas involving the hypergeometric functions. In this sequel, here, we aim at establishing two generalized integral formulas involving a Bessel functions of the first kind, which are expressed in terms of the generalized Wright hypergeometric function. Some interesting special cases of our main results are also considered.

Certain unified integrals associated with Bessel functions

Boundary Value Problems, 2013

A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Very recently, Ali gave three interesting unified integrals involving the hypergeometric function 2 F 1 . Using Ali's method, in this paper, we present two generalized integral formulas involving the Bessel function of the first kind J ν (z), which are expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our main results are also considered. MSC: Primary 33B20; 33C20; secondary 33B15; 33C05

Some Definite Integrals of the Product of Two Bessel Functions of the Second Kind: (Order Zero)

Mathematics of Computation

A new integral representation is derived for the expression J0(z)J0(Z) + Y0(z) ■ Ya(Z) and used to evaluate a number of integrals containing Y "(ax) Y¿bx). A supplementary table of integrals involving the function K0(x) in the integrand appears in the microfiche section of this issue. Jo 4 where g is the inverse K-L image of/. From Eqs. (10)-(16) of reference [5], we obtain

Some integrals involving Bessel functions

Arxiv preprint math/9307213, 1993

A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of products of three Bessel functions.

On certain integral formulas involving the product of Bessel function and Jacobi polynomial

Tamkang Journal of Mathematics, 2016

In the present paper, we establish some interesting integrals involving the product of Bessel function of the first kind with Jacobi polynomial, which are expressed in terms of Kampe de Feriet and Srivastava and Daoust functions. Some other integrals involving the product of Bessel (sine and cosine) function with ultraspherical polynomial, Gegenbauer polynomial, Tchebicheff polynomial, and Legendre polynomial are also established as special cases of our main results. Further, we derive an interesting connection between Kampe de Feriet and Srivastava and Daoust functions.

Some Finite Integrals Involving the Product of Bessel Function with Jacobi and Laguerre Polynomials

Communications of The Korean Mathematical Society, 2018

The main object of this paper is to set up two (conceivably) valuable double integrals including the multiplication of Bessel function with Jacobi and Laguerre polynomials, which are given in terms of Srivastava and Daoust functions. By virtue of the most broad nature of the function included therein, our primary findings are equipped for yielding an extensive number of (presumably new) fascinating and helpful results involving orthogonal polynomials, Whittaker functions, sine and cosine functions.

Unified integrals involving product of multivariable polynomials and generalized Bessel functions

Boletim da Sociedade Paranaense de Matemática

The aim of this paper is to evaluate two integral formulas involving a finite product of the generalized Bessel function of the first kind and multivariable polynomial functions which results are expressed in terms of the generalized Lauricella functions. The major results presented here are of general character and easily reducible to unique and well-known integral formulae.