On certain extended Exton's triple hypergeometric functions and associated bounding inequalities

Motivated by certain recent extensions of Euler's beta function, hypergeometric and confluent hypergeometric functions, we extend Exton's triple hypergeometric functions and investigate to present its properties such as various integral representations of Euler and Laplace type, Mellin transforms, Laguerre polynomial representation, transformation formulae and a recurrence relation. Also, by means of Luke's bounds for hypergeometric functions and various bounds upon the Bessel functions appearing in the kernels of the newly established integral representations, we deduce a set of bounding inequalities for the extended Exton's triple hypergeometric functions.
This is a joint work with Junesang Choi (Dongguk University, Gyeongju, South Korea).