Series reversion with Jacobi and Thron continued fractions

Abstract

Using ordinary and exponential generating functions, we explore the reversion of power series defined by $2$nd order recurrences. We express the reversions in terms of Jacobi and Thron continued fractions. We find relations with Eulerian expressions using a transformation of continued fractions.

26 Pages

References in corpus (1)

• Eulerian polynomials as moments, via exponential Riordan arrays