Fractional derivative of the multivariable polynomials.
Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function
2000 Mathematics Subject Classification: 26A33, 33C45This paper refers to a fractional order generalization of the classical Jacobi polynomials. Rodrigues’ type representation formula of fractional order is considered. By means of the Riemann–Liouville operator of fractional calculus fractional Jacobi functions are defined, some of their properties are given and compared with the corresponding properties of the classical Jacobi polynomials. These functions appear as a special case of a fractional Gauss...
Fractional Integration and Fractional Differentiation of the M-Series
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
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...
Fractional quantum integral inequalities.
From double Hecke algebra to analysis.
From holonomy of the Ising model form factors to -fold integrals and the theory of elliptic curves.
Fuchsian differential equation for the perimeter generating function of three-choice polygons.
Functional Analysis, Orthogonal Polynomials And A Theorem Of Markov.
Functional equation of a special Dirichlet series.
Functional identities for special functions of quasiconformal theory.
Further Generalization of Kobayashi's Gamma Function
In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z)
Further results on supernumary polylogarithmic ladders.