Soliton-generating τ-functions revisited

On composition of generating functions

In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...

The onset of e + e − → τ + τ − at threshold revisited

Batcher's odd-even exchange revisited: A generating functions approach

The celebrated odd-even exchange algorithm by Batcher provides the quantity average number of exchanges, which was a mystery a few years ago and is still tricky today. We provide an approach that is purely based on generating functions to provide an explicit expression. The asymptotic analysis was done several years ago but never published in a journal and is thus provided here. It is a combina...

Pfaff Τ -functions

6 Examples 32 6.1 Symmetric matrix integrals . . . . . . . . . . . . . . . . . . . 33 6.2 Quasiperiodic solutions . . . . . . . . . . . . . . . . . . . . . . 34 Department of Mathematics, Brandeis University, Waltham, Mass 02454, USA. Email: [email protected]. The support of a National Science Foundation grant # DMS-98-4-50790 is gratefully acknowledged. Department of Mathematics, Kyoto U...

QCD Analysis of Hadronic τ Decays Revisited

The calculation of perturbative corrections to the spectral moments observable in hadronic τ decays is reconsidered. The exact order-αs results and the resummation procedure of Le Diberder and Pich are compared with a partial resummation of the perturbative series based on the analysis of so-called renormalon chains. The perturbative analysis is complemented by a model-independent description o...