Definite Integrals, Some Involving Residue Theory Evaluated by Maple Code

Journal Article · Fri Jan 01 00:00:00 EST 2010 · Far East Journal of Theoretical Statistics

OSTI ID:978821

Bowman, Kimiko o ^[1]

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1. ORNL

The calculus of residue is applied to evaluate certain integrals in the range (-{infinity} to {infinity}) using the Maple symbolic code. These integrals are of the form {integral}{sub -{infinity}}{sup {infinity}} cos(x)/[(x{sup 2} + a{sup 2})(x{sup 2} + b{sup 2}) (x{sup 2} + c{sup 2})]dx and similar extensions. The Maple code is also applied to expressions in maximum likelihood estimator moments when sampling from the negative binomial distribution. In general the Maple code approach to the integrals gives correct answers to specified decimal places, but the symbolic result may be extremely long and complex.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 978821
• Journal Information: Far East Journal of Theoretical Statistics, Vol. 31, Issue 2
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
INTEGRALS
DISTRIBUTION
COMPUTER CALCULATIONS