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Recently, Srivastava, Saxena and Parmar [H. M. Srivastava, R. K. Saxena and R. K. Parmar, Some families of the incomplete  H -functions and the incompleteH  ¯{\overline{H}}   -functions and associated integral transforms and operators of fractional calculus with applications, Russ. J. Math. Phys. 25 2018, 1, 116–138] suggested incomplete  H -functions (IHF) that paved the way to a natural extension and decomposition of  H -function and other connected functions as well as to some important closed-form portrayals of definite and improper integrals of different kinds of special functions of physical sciences. In this article, our key aim is to present some new integral transform (Jacobi transform, Gegenbauer transform, Legendre transform and  δ{\mathsf{P}_{\delta}}   -transform) of this family of incomplete  H -functions. Further, we give several interesting new and known results which are special cases our key results.

On a family of the incomplete H -functions and associated integral transforms