Power series with sum-product Taylor coefficients and their resurgence algebra

Details Power series with sum-product Taylor coefficients and their resurgence algebra Power series with sum-product Taylor coefficients and their resurgence algebra

2009-12-18

arxiv.org/abs/0912.3687v2

Mathematics

Classical Analysis and ODEs

A number of typos have been rectified and chapter 6 has been expanded

Scientific paper

The present paper is devoted to power series of SP type, i.e. with coefficients that are syntactically sum-product combinations. Apart from their applications to analytic knot theory and the so-called "Volume Conjecture", SP-series are interesting in their own right, on at least four counts: (i) they generate quite distinctive resurgence algebras (ii) they are one of those relatively rare instances when the resurgence properties have to be derived directly from the Taylor coefficients (iii) some of them produce singularities that unexpectedly verify finite-order differential equations (iv) all of them are best handled with the help of two remarkable, infinite-order integral-differential transforms, "mir" and "nir".

Affiliated with

Also associated with

No associations

Rating

Power series with sum-product Taylor coefficients and their resurgence algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Power series with sum-product Taylor coefficients and their resurgence algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Power series with sum-product Taylor coefficients and their resurgence algebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-349814