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Some inequalities of the incomplete gamma and related functions. (English) Zbl 0934.33001
Many inequalities of some integrals which are related to the incomplete gamma function are established. The results improved some known results.

##### MSC:
 33B20 Incomplete beta and gamma functions 26D07 Inequalities involving other types of real functions 26D15 Inequalities for sums, series and integrals of real functions
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##### References:
 [1] Ji-Chang Kuang: Applied Inequalities (in Chinese), 2nd edition. Changsha (China): Hu- nan Education Press 1993. · Zbl 0744.26010 [2] Laforgia, A. and S. Sismondi: Monotonicity results and inequalities for the gamma and error functions. J. Comp. Appi. Math. 23 (1988), 25 - 33. · Zbl 0645.33001 · doi:10.1016/0377-0427(88)90328-7 [3] Mitrinovi, D. S.: Analytic Inequalities. New York et al.: Springer-Verlag 1970. [4] Feng Qi: Generalized weighted mean values with two parameters. Proc. Roy. Soc. London (Ser. A) 454 (1998), 2723 - 2732. · Zbl 0935.26014 · doi:10.1098/rspa.1998.0277 [5] Feng Qi: Monotonicity results and inequalities for the gamma and incomplete gamma functions. Math. Ineq. Appl. (2000) (to appear). · Zbl 1006.33001 [6] Feng Qi: A method of constructing inequalities about e’. Univ. Beograd. PubI. Elek- trotehn. Fak. Ser. Mat. 8 (1997), 16 - 23. · Zbl 0945.26027 [7] Feng Qi, Li-Hong Cui and Sen-Lin Xu: Some inequalities constructed by Tchebycheff’s integral inequality. Math. Ineq. AppI. 1999 (to appear). · Zbl 0943.26030 [8] Feng Qi and Bai-Ni Guo: Inequalities for generalized weighted mean values of convex function. Archiv Math. (to appear). · Zbl 0987.26019 [9] Feng Qi and Sen-Lin Cuo: Inequalities for the incomplete gamma and related functions. Math. Ineq. AppI. 2 (1999), 47 - 53. · Zbl 0916.33001 [10] Feng Qi and Shi-Qin Zhang: Note on monotonicity of generalized weighted mean values. Proc. Roy. Soc. London (Ser. A) (1999) (to appear). · Zbl 0942.26030 · doi:10.1098/rspa.1999.0449