Certain families of integral formulas involving Struve functions

Abstract

Recently, a large number of integral formulas involving Bessel functions and their extensions have been investigated. The objective of this paper is to establish four classes of integral formulas associated with the Struve functions, which are expressed in terms of the Fox-Wright function. Among a variety of special cases of the main results, we present only six integral formulas involving trigonometric and hyperbolic functions.

p , q -Extended Struve Function: Fractional Integrations and Application to Fractional Kinetic Equations

“…Presenting the last summation in (21) in terms of the Hadamard product (14) with the functions (16) and 17, we get the right side of (19). Now, we discuss the special cases of (19) as follows.…”

“…e Struve function is widely studied in the reference to properties and applications in several papers (see details [18][19][20][21][22]).…”

Some New Results Associated With the Generalized Lommel-Wright Function

“…(α 1 ) n , ...., (α p ) n z n (β 1 ) n , ...., (β q ) n n! = p F q (α 1 , ..., α p ; β 1 , ...., β q ; z), (4) where (ϑ) n is denote the Pochhammer symbol [15]. The series representation of the generalized Lommel Wright function as [5];…”

“…Various generalizations and cases of Lommel-Wright function have been investigated (see, for details, [1,14,7]). For more details of integral involving various special functions, one may be referred to the recent research papers [4,9,10,11] Integral formulas involving Lommel-Wright functions have been developed by many authors (see, e.g., [2,3,6,12]). In this sequel, here, we aim at establishing certain new generalized integral formula involving the generalized Lommel-Wright function J µ,m ν,λ (z) interesting integral formulas which are derived as special cases.…”

Some New Results Associated with the Generalized Lommel-Wright Function

“…Various generalizations and cases of Lommel-Wright function have been investigated (see, for details, [1,12,7]). For more details of integral involving various special functions, one may be referred to the recent research papers [4,9] Integral formulas involving Lommel-Wright functions have been developed by many authors (see, e.g., [2,3,6,10]). In this sequel, here, we aim at establishing certain new generalized integral formula involving the generalized Lommel-Wright function J µ,m ν,λ (z) interesting integral formulas which are derived as special cases.…”