Given positive integers n, k, and m, the (n, k)-th mrestrained Stirling number of the first kind is the number of permutations of an n-set with k disjoint cycles of length ≤ m. Inverting the matrix consisting of the (n, k)-th m-restrained Stirling number of the first kind as the (n+1, k +1)-th entry, the (n, k)-th m-restrained Stirling number of the second kind is defined. In this paper, the mu...

We explore the possibility of using the method of classical integral transforms to solve a class of q-difference-differential equations. The Laplace and the Mellin transform of q-derivatives are derived. The results show that the Mellin transform of the qderivative resembles most closely the corresponding expression in classical analysis, and it could therefore be useful in solving certain q-di...

and T (r, f), which is only true for finite order meromorphic functions. We have also obtained the proximity function and pointwise estimates of f(z+η)/f(z) which is a discrete version of the classical logarithmic derivative estimates of f(z). We apply these results to give new growth estimates of meromorphic solutions to higher order linear difference equations. This also allows us to solve an...

The boundedness character of positive solutions of two nonlinear fourth-order difference equations, which are particular cases of two large classes of difference equations by Stević, are studied in this paper.

We use four different methods involving recurrence relations for polynomials, orthogonal polynomials, symbolic summations and generating functions to determine a sum that originates in a calculation involving record statistics.

In this paper, we consider the nonlinear difference equation xn 1 f xn−l 1, xn−2k 1 , n 0, 1, . . . , where k, l ∈ {1, 2, . . . } with 2k / l and gcd 2k, l 1 and the initial values x−α, x−α 1, . . . , x0 ∈ 0, ∞ with α max{l − 1, 2k − 1}. We give sufficient conditions under which every positive solution of this equation converges to a not necessarily prime 2-periodic solution, which extends and ...

In this difference equation, Stability, Periodicity, boundedness, global Stability. We investigate some qualitative behavior of the solutions of the difference equation

We construct the Darboux transformation with Dihedral reduction group for the 2–dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry. Using formal diagonalisation of the Darboux matrix we ...

In this paper we present applications of some special numbers obtained from a difference equation of degree three, especially in the Coding Theory. As a particular case, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were extended to the generalized quaternions.

New characterizations are given for orthogonal polynomials on the unit circle and the associated measures in terms of the reflection coefficients in the recurrence equation satisfied by the polynomials.