Recursion Relation of Hyperelliptic Psi-Functions of Genus Two

TL;DR

This paper explores a new derivation of the recursion relation for hyperelliptic psi functions of genus two, extending Cantor's algebraic approach with an analytic method.

Contribution

It provides an alternative analytic derivation of the recursion relation for genus two hyperelliptic psi functions, complementing Cantor's algebraic method.

Findings

Derived a new analytic proof of the recursion relation

Extended methods from elliptic to hyperelliptic functions

Enhanced understanding of hyperelliptic psi functions

Abstract

A recursion relation of hyperelliptic psi functions of genus two, which was derived by D.G. Cantor (J. reine angew. Math. 447 (1994) 91-145), is studied. As Cantor's approach is algebraic, another derivation is presented as a natural extension of the analytic derivation of the recursion relation of the elliptic psi function.