Asymptotic evaluation of two families of integrals

Journal Article · Fri Jul 01 04:00:00 EDT 1977 · J. Math. Anal. Appl.; (United States)

DOI:https://doi.org/10.1016/0022-247X(77)90069-5· OSTI ID:7211642

Kaper, H G

The integrals f/sub mv/(tau) = ..integral../sub 0//sup infinity/ exp(-(t + tau))t/sup v/(ln t)/sup m/(t + tau)/sup -1/ dt and g/sub mv/(tau) = ..integral../sub 0//sup infinity/ exp(- parallel t - tau parallel)t/sup v/(ln t)/sup m/(t - tau)/sup -1/ dt are investigated for positive real values of the variable tau. Here, m is a nonnegative integer, v is a complex variable with Re(v) greater than -1. Both integrals are related to the complex integral PHI/sub m gamma/(z) = ..integral../sub 0//sup infinity/ exp(-(t - z))t/sup -//sup -gamma/(ln t)/sup m/(t - z)/sup -1/ dt with 0 less than or equal to Re(..gamma..) less than 1, the behavior of which is analyzed in detail. The results are applied to obtain asymptotic representations for f/sub mn/(tau) and g/sub mn/(tau), m and n both nonnegative integers, near tau = 0. The latter integrals play a role in the study of the equations of neutron transport and radiative transfer.

• Research Organization: Argonne National Lab., IL
• OSTI ID: 7211642
• Journal Information: J. Math. Anal. Appl.; (United States), Journal Name: J. Math. Anal. Appl.; (United States) Vol. 59:3; ISSN JMANA
• Country of Publication: United States
• Language: English

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