A Proof of the Koumandos--Ruscheweyh Conjecture

Yicen Ma

We prove the Koumandos--Ruscheweyh conjecture for every $0<\rho \le 1$. If $\nu (\rho )$ is the unique root in $(0,1]$ of ${\int }_0^{(1+\rho )\pi }{t}^{\mu -1}\sin (t-\rho \pi )\mathrm{d}t=0$, then $(1-z)^ρs_n^μ…