Asymptotic double subseries

Some Theorems on Subseries

1. Absolutely convergent series. A simple calculation reveals that the arithmetic mean value of all subsums (including the void sum) of a given finite sum sn=ui+U2 + • • • +un is equal to sn/2. In this section we shall show (see Theorem 1 below) that an integral mean value can be found, consistent with the preceding, for the sums of all infinite subseries of a given absolutely convergent series...

Double Asymptotic Scaling ’96

We review recent HERA data on the structure function F2 at small x and large Q . We show that the salient features of the data are revealed by comparing them to the double asymptotic scaling behaviour which F2 is predicted to satisfy in perturbative QCD. Invited talk given at

A Note on Subseries Convergence

Summing Curious, Slowly Convergent, Harmonic Subseries

The harmonic series diverges. But if we delete from it all terms whose denominators contain any string of digits such as “9”, “42”, or “314159”, then the sum of the remaining terms converges. These series converge far too slowly to compute their sums directly. We describe an algorithm to compute these and related sums to high precision. For example, the sum of the series whose denominators cont...

Double Asymptotic Scaling in Drell-Yan Processes

Double scaling may be observed in the Drell-Yan process at the Tevatron and in the ALICE detector at the Large Hadron Collider in a window of masses. In the double scaling limit of the cross section, the higher order QCD corrections are quite large, and are driven by the rise in gluon densities in the double scaling regime. The naive parton model cannot be valid even at asymptotic energies in t...