Analytic expressions for Debye functions and the heat capacity of a solid

TL;DR

This paper derives analytic expressions for the N-dimensional Debye function using the method of brackets, enabling detailed analysis of its asymptotic behavior at high and low temperatures.

Contribution

It introduces new analytic formulas for the Debye function applicable in multiple dimensions, facilitating better understanding of its temperature-dependent behavior.

Findings

Derived explicit formulas for N-dimensional Debye functions.

Analyzed asymptotic behavior at temperature extremes.

Provided tools for future thermodynamic studies of solids.

Abstract

Analytic expressions for the $N$-dimensional Debye function are obtained by the method of brackets. The new expressions are suitable for the analysis of the asymptotic behavior of this function, both in the high and low temperature limits.