Sufficient conditions are given for validity of the discrete Newton-Leibniz formula when the indefinite sum is obtained either by Gosper’s algorithm or by Accurate Summation algorithm. It is shown that sometimes a polynomial can be factored from the summand in such a way that the safe summation range is inreased.

In recent years, the problem of symbolic summation has received much attention due to the exciting applications of Zeilberger’s method for definite hypergeometric summation. This lead to renewed interest in the central part of the algorithmic machinery, Gosper’s “classical” method for indefinite hypergeometric summation. We review some of the recent (partly unpublished as yet) work done in this...

The atom-bond connectivity index of graph is a topological index proposed by Estrada et al. as ABC (G)  uvE (G ) (du dv  2) / dudv , where the summation goes over all edges of G, du and dv are the degrees of the terminal vertices u and v of edge uv. In the present paper, some upper bounds for the second type of atom-bond connectivity index are computed.

We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeomet-ric series. We extend two of our identities, by analytic continuation, to bilateral summation formulae which contain Ramanujan's 1 ψ 1 summation and a very-well-poised 4 ψ 6 summation as spec...

We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeometric series. We extend two of our identities, by analytic continuation, to bilateral summation formulae which contain Ramanujan’s 1ψ1 summation and a very-well-poised 4ψ6 summation as special c...

PURPOSE To evaluate scotopic retinal organization in retinopathy of prematurity (ROP) through a study of spatial summation. METHODS Thresholds for a range of stimulus diameters (0.4°-10°) were measured using a two alternative, spatial, forced choice psychophysical procedure. The critical diameter (DCRIT) for complete summation was estimated in subjects with a history of severe ROP (N = 7) and...