The solvability of a k-dimensional system of difference equations of interest, which extends several recently studied ones, is investigated. A general sufficient condition for the solvability of the system is given, considerably extending some recent results in the literature.

The Legendre-Stirling numbers are the coeffi cients in the integral Lagrangian symmetric powers of the classical Legendre second-order differential expression. In many ways, these numbers mimic the classical Stirling numbers of the second kind which play a similar role in the integral powers of the classical second-order Laguerre differential expression. In a recent paper, Andrews and Littlejoh...

Differential-difference equations (DDEs) of the form u n (t) = Fn(t, un+a, . . . , un+b) with k ≥ 2 are studied for Lie symmetries and preliminary classification. Explicit forms of equations are given for those admitting at least one intrinsic Lie symmetry. An algorithmic mechanism is also proposed to automate the symmetry calculation for fairly general DDEs via computer algebras.

and Applied Analysis 3 Then (a) for any L ∈ (N,M), there exist θ ∈ (0, 1) and T ≥ n 0 + τ + β such that for each x 0 = {x 0n } n∈N β ∈ A(N,M), the Mann iterative sequence with errors {x m } m∈N 0 = {x mn } (m,n)∈N 0 ×N β generated by the scheme

Using elliptic modular functions, Kronecker proved a number of recurrence relations for suitable class numbers of positive binary quadratic forms. For instance if F (N) denotes the number of uneven classes of positive binary quadratic forms with determinant −N, then