- Title
- Uniform bounds for the complementary incomplete gamma function
- Creator
- Borwein, Jonathan M.; Chan, O-yeat
- Relation
- Mathematical Inequalities and Applications Vol. 12, Issue 1, p. 115-121
- Publisher Link
- http://dx.doi.org/10.7153/mia-12-10
- Publisher
- Element d.o.o.
- Resource Type
- journal article
- Date
- 2009
- Description
- We prove upper and lower bounds for the complementary incomplete gamma function Г(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, |Г(a, z)| is of order |z|a−1e−Re(z), and extends an upper estimate of Natalini and Palumbo to complex values of z.
- Subject
- incomplete gamma function; inequalities; uniform bounds
- Identifier
- http://hdl.handle.net/1959.13/940194
- Identifier
- uon:12968
- Identifier
- ISSN:1331-4343
- Language
- eng
- Reviewed
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