Séries d'Eisenstein et transcendance
Several properties of generalized Fox's H-functions and their applications
Siebzehntheilung des Lemniscatenumfangs durch alleinige Anwendung von Lineal und Cirkel.
Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions
MSC 2010: 35R11, 42A38, 26A33, 33E12The method of integral transforms based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is utilized for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the Weyl space-fractional operator. The solutions obtained are in integral form whose kernels are Green functions expressed in terms of the Fox H-functions....
Solvable rational potentials and exceptional orthogonal polynomials in supersymmetric quantum mechanics.
Some characterizations of q-factorial functions.
Some characterizations of q-factorial functions.
Some elliptic function identities
Some generating functions for polynomials
Some generating functions of modified Bessel polynomials from the view point of Lie group.
Some inequalities for the Hersch-Pfluger distortion function.
Some problems and solutions involving Mathieu's series and its generalizations.
Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective
Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.Mittag-Leffler functions and their generalizations appear in a large variety of problems in different areas. When we move from total differential equations to fractional equations Mittag-Leffler functions come in naturally. Fractional reaction-diffusion problems in physical sciences and general input-output models in other disciplines are some of the examples in this direction. Some basic properties of Mittag-Leffler functions are...
Some properties of the jacobian sn z function.
Using some results of the theory of functional equations we deduce some properties of the Jacobian sn z function which seem to be new. Some functional equations have also been found which are fulfilled by the sn z function which the author did not find in the literature.
Some relations on Humbert matrix polynomials
The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix representations, matrix differential equation and expansions in series of some relatively more familiar matrix polynomials of Legendre, Gegenbauer, Hermite, Laguerre and modified Laguerre. Finally, some definitions of generalized Humbert matrix polynomials...
Some relations satisfied by Hermite-Hermite matrix polynomials
The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the Hermite-Hermite...
Some sums of Legendre and Jacobi polynomials
We prove identities involving sums of Legendre and Jacobi polynomials. The identities are related to Green’s functions for powers of the invariant Laplacian and to the Minakshisundaram-Pleijel zeta function.
Some theta functions identities associated with the modular equations of degree 5.
Special values of the dilogarithm function
Spectral curves of operators with elliptic coefficients.