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Finite monodromy of Pochhammer equation

Yoshishige Haraoka (1994)

Annales de l'institut Fourier

We consider the monodromy group G of the Pochhammer differential equation 𝒫 . Let 𝒫 p be the reduce equation modulo a prime p . Then we show that G is finite if and only if 𝒫 p has a full set of polynomial solutions for almost all primes p .

Fractional Calculus of P-transforms

Kumar, Dilip, Kilbas, Anatoly (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99The fractional calculus of the P-transform or pathway transform which is a generalization of many well known integral transforms is studied. The Mellin and Laplace transforms of a P-transform are obtained. The composition formulae for the various fractional operators such as Saigo operator, Kober operator and Riemann-Liouville fractional integral and differential operators with P-transform are proved. Application of the P-transform in reaction rate...

Fractional Integration and Fractional Differentiation of the M-Series

Sharma, Manoj (2008)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 33C60, 44A15In this paper a new special function called as M-series is introduced. This series is a particular case of the H-function of Inayat-Hussain. The M-series is interesting because the pFq -hypergeometric function and the Mittag-Leffler function follow as its particular cases, and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Let us note that the Mittag-Leffler ...

Fractional Integration of the Product of Bessel Functions of the First Kind

Kilbas, Anatoly, Sebastian, Nicy (2010)

Fractional Calculus and Applied Analysis

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine...

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