On polynomials with simple trigonometric formulas.
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
On product of generalized Appell polynomials
On pseudo Hermite matrix polynomials of two variables.
On -analogs of recursions for the number of involutions and prime order elements in symmetric groups.
On -Euler numbers related to the modified -Bernstein polynomials.
On -operators and summation of some -series.
On -summation and confluence
This paper is divided in two parts. In the first part we study a convergent -analog of the divergent Euler series, with , and we show how the Borel sum of a generic Gevrey formal solution to a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of a corresponding -difference equation. In the second part, we work under the assumption . In this case, at least four different -Borel sums of a divergent power series solution of an irregular singular...
On q–Analogues of Caputo Derivative and Mittag–Leffler Function
Mathematics Subject Classification: 33D60, 33E12, 26A33Based on the fractional q–integral with the parametric lower limit of integration, we consider the fractional q–derivative of Caputo type. Especially, its applications to q-exponential functions allow us to introduce q–analogues of the Mittag–Leffler function. Vice versa, those functions can be used for defining generalized operators in fractional q–calculus.
On q-asymptotics for q-difference-differential equations with Fuchsian and irregular singularities
This work is devoted to the study of a Cauchy problem for a certain family of q-difference-differential equations having Fuchsian and irregular singularities. For given formal initial conditions, we first prove the existence of a unique formal power series X̂(t,z) solving the problem. Under appropriate conditions, q-Borel and q-Laplace techniques (firstly developed by J.-P. Ramis and C. Zhang) help us in order to construct actual holomorphic solutions of the Cauchy problem whose q-asymptotic expansion...
On q-Euler numbers, q-Salié numbers and q-Carlitz numbers
On q-Laplace Transforms of the q-Bessel Functions
Mathematics Subject Classification: 33D15, 44A10, 44A20The present paper deals with the evaluation of the q-Laplace transforms of a product of basic analogues of the Bessel functions. As applications, several useful special cases have been deduced.
On quasi-periods of abelian functions with complex multiplication
On rational classical orthogonal polynomials and their application for explicit computation of inverse Laplace transforms.
On rational De Rham cohomology associated with the generalized airy function
On recurrence relations for radial wave functions for the -th dimensional oscillators and hydrogenlike atoms: analytical and numerical study.
On Reimer recurrences
On rules of derivation with complex order for analytic and branched functions
On solutions of differential equations with ``common zero'' at infinity
The zeros of the solution of the differential equation are investigated when , and has some monotonicity properties as . The notion is introduced also for real, too. We are particularly interested in solutions which are “close" to the functions , when is large. We derive a formula for and apply the result to Bessel differential equation, where we introduce new pair of linearly independent solutions replacing the usual pair , . We show the concavity of for and also...
On solving general algebraic equations by integrals of elementary functions.