The perturbative expansion series in coupling constant in QED is divergent and is expected to be, at the best, conditionally convergent. The 1/Nf series expansion, where Nf is the number of flavours, defines a rearrangement of this perturbative series, and therefore, its convergence would serve as a proof that the perturbative series is, in fact, conditionally convergent.Unfortunately, the 1/Nf...

In 1968, M. Artin proved that any formal power series solution of a system of analytic equations may be approximated by convergent power series solutions. Motivated by this result and a similar result of Płoski, he conjectured that this remains true when we replace the ring of convergent power series by a more general ring. This paper presents the state of the art on this problem, aimed at non-...

By means of a variational approach we find new series representations both for well known mathematical constants, such as π and the Catalan constant, and for mathematical functions, such as the Rie-mann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar ...

By means of a variational approach we find new series representations both for well known mathematical constants, such as π and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar e...

By means of a variational approach we find new series representations both for well known mathematical constants, such as π and the Catalan constant, and for mathematical functions, such as the Rie-mann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar ...

We provide a general class of tests for correlation in time series, spatial, spatio-temporal and cross-sectional data. We motivate our focus by reviewing how computational and theoretical di¢ culties of point estimation mount as one moves from regularly-spaced time series data, through forms of irregular spacing, and to spatial data of various kinds. A broad class of computationally simple test...

Slowly convergent series and sequences as well as divergent series occur quite frequently in the mathematical treatment of scientific problems. In this report, a large number of mainly nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series are discussed. Some of the sequence transformations of this report as for instance Wynn’s ǫ algorithm o...

By means of a variational approach we find new series representations both for well known mathematical constants, such as π and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar e...

We discuss Levin-type sequence transformations {sn} → {sn} that depend linearly on the sequence elements sn, and nonlinearly on an auxiliary sequence of remainder estimates {ωn}. If the remainder estimates also depend on the sequence elements, non-linear transformations are obtained. The application of such transformations very often yields new sequences that are more rapidly convergent in the ...

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 ...