Currently displaying 1 – 15 of 15

Showing per page

Order by Relevance | Title | Year of publication

Resurgence of the Euler-MacLaurin summation formula

Ovidiu CostinStavros Garoufalidis — 2008

Annales de l’institut Fourier

The Euler-MacLaurin summation formula compares the sum of a function over the lattice points of an interval with its corresponding integral, plus a remainder term. The remainder term has an asymptotic expansion, and for a typical analytic function, it is a divergent (Gevrey-1) series. Under some decay assumptions of the function in a half-plane (resp. in the vertical strip containing the summation interval), Hardy (resp. Abel-Plana) prove that the asymptotic expansion is a Borel summable series,...

Resurgence of the Kontsevich-Zagier series

Ovidiu CostinStavros Garoufalidis — 2011

Annales de l’institut Fourier

The paper is concerned with the resurgence of the Kontsevich-Zagier series f ( q ) = n = 0 ( 1 - q ) ( 1 - q n ) We give an explicit formula for the Borel transform of the power series when q = e 1 / x from which its analytic continuation, its singularities (all on the positive real axis) and the local monodromy can be manifestly determined. We also give two formulas (one involving the Dedekind eta function, and another involving the complex error function) for the right, left and median summation of the Borel transform....

Page 1

Download Results (CSV)