Lattice Green Function (at 0) for the 4d Hypercubic Lattice

TL;DR

This paper derives the generating function for recurrent Polya walks on a 4D hypercubic lattice using special functions, providing insights into the enumeration and properties of these walks.

Contribution

It introduces a novel expression of the generating function as a Kampe-de-Feriet function for 4D lattice walks, expanding theoretical understanding.

Findings

Explicit form of the generating function as a Kampe-de-Feriet function

Enumeration of properties of 4D lattice walks

Theoretical insights into walk recurrence and structure

Abstract

The generating function for recurrent Polya walks on the four dimensional hypercubic lattice is expressed as a Kampe-de-Feriet function. Various properties of the associated walks are enumerated.