Abstract:
In article the sedate assessment of a high order for function $V(x)=\frac{3}{\Gamma(\frac16)}\int_x^\infty e^{s^{-6}}\,ds$, where $\Gamma(x)$ — Euler's gamma function is established. It is shown that for all valid $x$ and all $k$ from an interval $[1;\sqrt[6]{4}]$ fairly an inequality $V^{4}(x)<V(kx)$. Besides it is established that the main result remains at $0\le k<1$ for any positive $x$.
Keywords:integrated inequalities, gamma function, sedate estimates, not own integral, logarithmic convex function.