The discussion revolves around the series involving gamma functions, specifically the sum of the form $\sum_{n=0}^{\infty} \frac{\Gamma(a+n)\Gamma(b+n)}{n! \Gamma(c+n)}$ under the condition $c-a-b > 0$. It is noted that this series can be interpreted through Gauss' hypergeometric theorem, which provides a connection to hypergeometric functions. The transformation of the series into a form involving beta functions and integrals is discussed, leading to a simplified expression for the sum. The final result shows that the series equals $\frac{\Gamma(a) \Gamma(b) \Gamma(c-a-b)}{\Gamma(c-a) \Gamma(c-b)}$. This highlights the relationship between gamma functions and hypergeometric series in mathematical analysis.