Double Series Involving Binomial Coefficients and the Sine Integral

2010/09/01 by John M. Campbell, Campbell, John M.
Mathematics · #40G99 #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT #msc:40G99

paper · pdf · doi:10.48550/arxiv.1009.0236

openalex publication_date 2010/09/01 · arxiv created 2010/09/16 · arxiv updated 2010/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By dividing hypergeometric series representations of the inverse sine by sin^-1 (x) and integrating, new double series representations of integers and constants arise. Binomial coefficients and the sine integral are thus combined in double series.

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