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In the present study we deal with certain integral properties pertaining to a general class of polynomials, Aleph function, H-function, and the generalized M-Series. The main outcomes presented here are nature wise basic and unified and are possibly useful in many fields particularly statistical mechanics, probability theory, electrical networks, etc. The integrals involved here include several types of Feynman integrals, the precise division of Gaussian models in statistical mechanics, and many other special case functions. These results provide numerous corresponding remarkable results, such as simpler special functions and polynomials, which are special cases of expressions.
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