Abel's Functional Equation and Interrelations

2025/03/01 by Finch, Steven
#26A18 #39-08 #39B22 (Primary) 11B37 #41A60 #65D20 (Secondary) #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.00579

Abstract

Convex solutions A,B,I,J of four Abel equations are numerically studied. We do not know exact formulas for any of these functions, but conjecture that A,B and I,J are closely related. [Corrigendum at end.]

Related

• A survey on the hypertranscendence of the solutions of the Schröder's, Böttcher's and Abel's equations
• General Solutions of the Abel Differential Equations
• Notes on Three Formulas of Abel
• Abelian functional equations, planar web geometry and polylogarithms
• Outcomes of the Abel Identity