Analytical Solution to Improper Integral of Divergent Power Functions Using The Riemann Zeta Function

Farhad Aghili, Siamak Tafazoli

This paper presents an analytical closed-form solution to improper integral $\mu (r)={\int }_0^{\infty }{x}^{r}dx$, where $r\ge 0$. The solution technique is based on splitting the improp…