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Zeitschrift für Analysis und ihre Anwendungen

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Volume 18, Issue 3, 1999, pp. 793–799
DOI: 10.4171/ZAA/914

Published online: 1999-09-30

Some Inequalities of the Incomplete Gamma and Related Functions

Feng Qi[1] and Jia-Qiang Mei[2]

(1) Jiaozuo Institute of Technology, Jiaozuo City, Henan, China
(2) University of Science and Technology of China, Hefei City, Anhui, China

In the article, many inequalities of the integrals $$\int^{\infty}_x e^{–t^p} dt, \ \ \ \int^x_0 e^{–t^p}, \ \ \ \int^x_0 e^{t^p} dt$$ for $p > 0$, which are related to the incomplete gamma function, are established. The approach used in the paper could yield more particular inequalities of the above functions. Some known results are generalized, extended or refined.

Keywords: Inequalities, incomplete gamma function, complementary error function

Qi Feng, Mei Jia-Qiang: Some Inequalities of the Incomplete Gamma and Related Functions. Z. Anal. Anwend. 18 (1999), 793-799. doi: 10.4171/ZAA/914