Series reversion with Jacobi and Thron continued fractions

2021/07/29 by Paul Barry, Barry, Paul
Chemistry · Mathematics · #11B83 #1536 #30B10 #30B70 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT) #Primary 05A15 #Secondary 11B39

paper · pdf · doi:10.48550/arxiv.2107.14278

openalex publication_date 2021/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using ordinary and exponential generating functions, we explore the reversion of power series defined by 2nd 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.

Citations

• The on-line encyclopedia of integer sequences

Related

• On a two-valued sequence and related continued fractions in power series fields
• Riordan arrays and Jacobi and Thron continued fractions
• Observations on continued fractions
• Continued Fractions for Square Series Generating Functions
• Bifurcating Continued Fractions II