Year: 2023
Type: preprint
Abstract: We set the scene with known values and functional relations for dilogarithms, trilogarithms and polylogarithms of various orders, along with more recent Euler sum values and multidimensional computations paying homage to the three late Professors Borwein \textit{et al.}. We then apply many of these sum values to tabulate some sixty new combinatorial identities for weighted partitions into Visible Point Vectors in 2D, 3D, 4D and 5D cases suggesting new $n$D first hyperquadrant and hyperpyramid lattice point identities.
Source: arXiv (Cornell University)
Author: Campbell, Geoffrey B.
Institution: Australian National University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4379539352