By the telescoping method, Sun has recently given some hypergeometric series whose sums are related to π. We investigate these from point of view Gosper's algorithm. Given a term tk, we consider Gosper summability r(k)tk for r(k) being rational function k. give an upper bound and lower on degree numerator such that is summable. also show denominator can be read off representation tk+1/tk. Based...

We construct an example of a series that is Abel summable but whose associated power series does not converge on angular sectors. We also give some related results.

Measurements of relaxed expiratory volume in one second (REV1.0) and forced inspiratory volume in one second (FIV1.0) were made on 50 subjects on two occasions to know the variability of these procedures in the individual subject. The mean coefficients of variation for REV1.0 and FIV1.0 were 6740' and 892%, respectively. The 95% confidence limit of difference between highest readings obtained o...

We consider the problem of forecasting the next (observable) state of an unknown ergodic dynamical system from a noisy observation of the present state. Our main result shows, e.g., that support vector machines (SVMs) using Gaussian RBF kernels can learn the best forecaster from a sequence of noisy observations if a) the unknown observational noise processes is bounded and has a summable α-mixi...

We introduce the vector-valued sequence spaces w∞ Δ, F,Q, p, u , w1 Δ, F,Q, p, u , and w0 Δ, F,Q, p, u , S q u and S q 0u, using a sequence of modulus functions and the multiplier sequence u uk of nonzero complex numbers. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly Δuq-Cesàro summable with respect to the modulus function f then it is ...