More trigonometric integrals

Abstract:

Integrals of the form \[ \int _0^{\pi /2} {{e^{ip\theta }}{{\cos }^q}\theta d\theta ,\quad \int _0^{\pi /2} {{e^{ip\theta }}{{\sin }^q}\theta d\theta } } \] (p real, $\operatorname {Re} (q) > - 1$) are expressed in terms of Gamma and hypergeometric functions for integer and noninteger values of q and p. The results include those of [2] as special cases.