unexpected logarithmic identities and other surprises

TL;DR

This paper explores surprising mathematical identities involving integrals, involutions, and hypergeometric functions, revealing unexpected logarithmic relations and other mysterious objects inspired by prior research in integrals and cellular automata.

Contribution

It introduces novel logarithmic identities and investigates their connections to hypergeometric functions and involutions, expanding understanding of these mathematical structures.

Findings

Discovery of new logarithmic identities

Identification of hypergeometric functions with linear regimes

Revealing connections between integrals and cellular automata

Abstract

This is a journey through integrals of involutions and surprising consequences of the Lagrange inversion theorem. On the way, we meet unexpected logarithmic identities, hypergeometric functions with a linear regime and other mysterious objects. This study was inspired by some results from the fascinating article A.E. Holroyd, T.M. Liggett and D. Romik, Integrals, Partitions, and Cellular Automata, Transactions of the American Mathematical Society, 356-8, 3349-3368, 2004