Wallis m-integrals and their properties

Resumen

This paper investigates asymptotic behaviour of the m-Wallis integrals

\[\ W(m,k) = \int_{0}^{\frac{\pi}{2}} x^{m}\cos^k x \, dx, m \in \mathbb{N} \cup \{0\},k \in \mathbb{N}.\]