16 июн. 2012 г. · Lower and upper bounds for the incomplete gamma function are also derived. Bounds for the error function erf are also established.

16 июн. 2012 г. · The goal of this paper is to establish inequalities and bounds for the incomplete gamma function. In Sect. 2 we provide defini- tions which ...

13 мая 2020 г. · Lower and upper bounds B_a(x) on the incomplete gamma function \Gamma(a,x) are given for all real a and all real x>0. These bounds B_a(x) are exact.

These inequalities and bounds are based on continued fraction expansions of the incomplete gamma function (Sections 2 and 3). Comparisons between the two sets ...

then we have the following inequalities: • if T(x) > 0 for x > 0, then Γ(a, x) > xae−xq(x); • if T(x) < 0 for x > 0, then Γ(a, x) < xae−xq(x). Proof.

The approach used in the paper could yield more particular inequalities of the above functions. Some known results are generalized, extended or refined.

... incomplete gamma function r(a,x) ta-le-tdt, namely, j et dt = -r ( x). Gautschi [3] showed that the inequalities (1.3) can be used to derive bounds for the.

The lower bounds of inequalities (4) and (18) do not imply each other. The difference between the logarithms of the lower bounds in inequalities (4) and. (18) ...

22 окт. 2024 г. · Lower and upper bounds Ba(x) on the incomplete gamma function Γ(a,x) are given for all real a and all real x>0. These bounds Ba(x) are exact ...

16 дек. 2022 г. · Abstract. In this paper, we present new inequalities and bounds involving the incomplete gamma function and related functions.