# Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics > 2001 > 131 > 1-2 > 195-222

_{n}

_{,}

_{α}

_{,}

_{β}∫0π/2ln

^{n}(sin

^{α}θcos

^{β}θ)dθ, where n is a nonnegative integer, are provided as examples. We focus in particular on the integrals I

_{n}∫0π/2ln

^{n}sinθdθ, which have been frequently discussed...

Journal of Computational and Applied Mathematics > 2001 > 133 > 1-2 > 495-505

Journal of Computational and Applied Mathematics > 2001 > 133 > 1-2 > 387-396

_{1}+x

_{2})=<Γ(1+x

_{1})Γ(1+x

_{2})<Γ(1+x

_{1}+x

_{2})for x

_{1},x

_{2}>0 and x

_{1}.x

_{2}=1. Finally, we study the possible extension to k variables of the lower bound above.

Journal of Computational and Applied Mathematics > 2001 > 135 > 2 > 225-240

^{6}-(8x

^{3}+4x

^{2}+x), where g(x)=(e/x)

^{x}Γ(1+x)/π, is studied. It is proved that on the interval (1,~) the function h(x) is increasing monotonically from h(1)=0.0111976... to h(~)=1/30=0.0333....