An exactly solvable self-convolutive recurrence

Details An exactly solvable self-convolutive recurrence An exactly solvable self-convolutive recurrence

2011-03-25

arxiv.org/abs/1103.4936v1

Mathematics

Combinatorics

Scientific paper

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function $U(a,b,z)$. By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the $n$th coefficient is expressed as the $(n-1)$th moment of a measure, and also as the trace of the $(n-1)$th iterate of a linear operator. Applications of these sequences, and hence of the explicit solution provided, are found in quantum field theory as the number of Feynman diagrams of a certain type and order, in Brownian motion theory, and in combinatorics.

Affiliated with

Also associated with

No associations

Rating

An exactly solvable self-convolutive recurrence 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 An exactly solvable self-convolutive recurrence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An exactly solvable self-convolutive recurrence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-570767