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Uniform Bounds for the Complementary Incomplete Gamma Function

Borwein, Jonathan M. and Chan, O-Yeat (2009) Uniform Bounds for the Complementary Incomplete Gamma Function. Mathematical Inequalities and Applications, 12 . pp. 115-121.

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    Abstract

    We prove upper and lower bounds for the complementary incomplete gamma function $\G(a,z)$ with complex parameters $a$ and $z$. Our bounds are refined within the circular hyperboloid of one sheet $\{(a,z):|z|>c|a-1|\}$ with $a$ real and $z$ complex. Our results show that within the hyperboloid, $|\G(a,z)|$ is of order $|z|^{a-1}e^{-\Re(z)}$, and extends an upper estimate of Natalini and Palumbo to complex values of $z$.

    Item Type: Article
    Additional Information: pubdom FALSE
    Uncontrolled Keywords: Incomplete Gamma Function, Inequalities, Uniform Bounds, AARMS
    Subjects: 33-xx Special functions > 33Bxx Elementary classical functions
    Faculty: UNSPECIFIED
    Depositing User: O-Yeat Chan
    Date Deposited: 22 Feb 2007
    Last Modified: 05 Jan 2015 16:29
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/335

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