The Umbral operator and the integration involving generalized Bessel-type functions

Abstract

Abstract:The main purpose of this paper is to introduce a class of new integrals involving generalized Bessel functions and generalized Struve functions by using operational method and umbral formalization of Ramanujan master theorem. Their connections with trigonometric functions with several distinct complex arguments are also presented.

A note on degenerate Euler polynomials arising from umbral calculus

“…In particular, authors found some combinatorial identities between Catalan-Daehee polynomials and special polynomials by using degenerate umbral calculus (see [15]), and in [32], authors introduced a class of new integrals involving generalized Bessel functions and generalized Struve functions by using operational method and umbral formalization of Ramanujan master theorem.…”

From Circular to Bessel Functions: A Transition through the Umbral Method

“…In the previous sections, we have developed a formalism capable of providing a unified point of view to apparently different functions; analogous ideas have also recently appeared in the literature [13], and the possibilities offered by the technique may be considered promising, if properly developed. To corroborate the previous statement, we recall that, aside from yielding a common environment for the Bessel congeries and their associates, the method allows for the derivation of previously unknown sum rules of lacunary Laguerre polynomials [14].…”

Inequalities on an extended Bessel function

“…A solution of the homogeneous modified Bessel equation gives the modified Bessel function of order p Because of its importance, the Bessel function and other special functions are of continued interest to the wider scientific community. The Bessel function and its variations have gone through several generalizations, see, for example, [ 1 – 6 ]. These generalized functions have also been framed as complex-valued analytic functions in the unit disk.…”