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JOURNALS // Meždunarodnyj naučno-issledovatel'skij žurnal // Archive

Meždunar. nauč.-issled. žurn., 2015 Issue 10-4(41), Pages 25–27 (Mi irj87)

PHYSICS AND MATHEMATICS

About one integrated assessment

R. V. Puchnin, Yu. V. Shvets, N. V. Miller

Siberian Transport University

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.

DOI: 10.18454/IRJ.2015.41.142



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