On certain integral formulas involving the product of Bessel function and Jacobi polynomial (original) (raw)

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.

Integral Formulas Involving Product of General Class of Polynomials and Generalized Bessel Function

Sohag Journal of Mathematics, 2016

By means of the Oberhettinger integral, certain generalized integral formulae involving product of generalized k-Bessel function w γ,α k,v,b,c (z) and general class of polynomials S m n [x] are derived, the results of which are expressed in terms of the generalized Wright hypergeometric functions. Several new results are also obtained from the integrals presented in this paper.

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.

Certain unified integrals involving a product of Bessel functions of the first kind

A remarkably large number of integrals involving a product of certain combinations of Bessel functions of several kinds as well as Bessel functions, themselves, have been investigated by many authors. Motivated the works of both Garg and Mittal and Ali, very recently, Choi and Agarwal gave two interesting unified integrals involving the Bessel function of the first kind Jν (z). In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present two generalized integral formulas involving a product of Bessel functions of the first kind, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. Some interesting special cases and (potential) usefulness of our main results are also considered and remarked, respectively.

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.

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.

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.