A Family of Generating Functions for Reciprocal Binomial Coefficients and Its Applications
Abstract
A generating function for reciprocal binomial coefficients is written down, integral representations of this function are obtained, generating functions for sums of reciprocal binomial coefficients are derived, new identities are obtained, including identities connecting reciprocal binomial coefficients with harmonic numbers and Fibonacci numbers. The application of the found functions for evaluating infinite numerical sequences involving reciprocal binomial coefficients is demonstrated.
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Combinatorial Mathematics
Mathematical functions and polynomials
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 8 February 2026
- Language
- EN
- Document type
- Preprint