Summation of imprecise numbers

Summation formulae involving harmonic numbers

Several summation formulae for finite and infinite series involving the classical harmonic numbers are presented. The classical harmonic numbers are defined by

Summation Formulae and Stirling Numbers

We exploit methods of operational and combinatorial nature to get a class of summation formulae involving special functions and polynomi-als. The results obtained in this paper complete and integrate previous investigations obtained with different methods.

Entropy Numbers of Certain Summation Operators

Given nonnegative real sequences a = (αk)k∈Z and b = (βk)k∈Z we study the generated summation operator Sa,b(x) := ( αk [∑ l<k βlxl ]) k∈Z , x = (xk)k∈Z , regarded as a mapping from `p(Z) to `q(Z). We give necessary and sufficient conditions for the boundedness of Sa,b and prove optimal estimates for its entropy numbers relative to the summation properties of a and b. Our results are applied to ...

Some summation formulas involving harmonic numbers and generalized harmonic numbers

Summation identities for representation of certain real numbers

The background and motivation for studying this problem lies in finding the zeros of the jth-order generalized Fibonacci polynomial defined by Fj(x) = x j−1 − ··· − x− 1. Dubeau [1] and Flores [3] have shown that the positive roots of Fj(x) are of the form 2−O(2− j). Grossman and Narayan [4] have proven that the single negative zero of Fj(x) has the form −1+O( j−1) for j even and tends to −1 mo...