Abstract
The 𝒫-transform or pathway transform, which is a generalization of many existing integral transforms, is considered. The 𝒫-transform is obtained by using the pathway model introduced by Mathai in 2005. The basic properties of the 𝒫-transform are obtained. The composition formula for the differential operator with the 𝒫-transform is proved. Connection of the type-2 𝒫-transform with the H-transform is also established. As examples, type-2 𝒫-transforms of some generalized special functions are obtained. The special cases of the kernal function of the 𝒫-transform are the extended non-resonant thermonuclear reaction rate probability integral in the Maxwell–Boltzmann case and cut-off case, which is used in astrophysics.
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