Double Series Involving Binomial Coefficients and the Sine Integral

TL;DR

This paper introduces novel double series representations that connect binomial coefficients and the sine integral through hypergeometric series manipulations and integration.

Contribution

It presents new double series formulas involving binomial coefficients and the sine integral derived from hypergeometric series and integration techniques.

Findings

New double series representations for integers and constants.

Combination of binomial coefficients with the sine integral in series form.

Methodology involving division of hypergeometric series and integration.

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.