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Further Generalizations Of Gamma, Beta And Related Functions
(Univ Prishtines, 2018) Sahin, Recep; Yaggi, Oguz; Yagbasan, Baki; Kiymaz, I. Onur; Cetinkaya, Aysegul
In this paper, we present further generalizations of gamma and beta functions by adding extra parameters to their integral representations. Then we introduce new generalizations of hypergeometric and confluent hypergeometric functions by using new beta function. We also obtain many interesting properties such as integral transforms, differentiation formulas, Mellin transforms, transformation formulas, differential and difference relations and a summation formula.
Generalized M-Series And Its Certain Properties
(Univ Prishtines, 2019) Kiymaz, I. Onur; Cetinkaya, Aysegul; Sahin, Recep
In this paper, we introduce a generalization of M-series by using the extended beta function. We also obtain its certain properties such as integral representations, derivative formulas, fractional integral and derivative formulas, Laplace, Mellin and Beta transforms.