A Set of Identities for a Class of Alternating Binomial Sums Arising in Computing Applications

TL;DR

This paper derives general identities for alternating binomial sums relevant to algorithm analysis, using integral and special function techniques, unifying and extending previous results.

Contribution

It introduces a broad set of identities for alternating binomial sums, employing integral and special functions, and generalizes several known cases.

Findings

Unified identities for alternating binomial sums

Extension of previous known results

Methodology applicable to broader cases

Abstract

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to subsume several previously known cases. Extensions of the method are apparent and are outlined.