Asymptotics of a class of integrals

2013/02/02 by A. G. Ramm, Ramm, A. G.
Mathematics · Physics and Astronomy · #41A60 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:41A60

paper · pdf · doi:10.48550/arxiv.1302.0391

arxiv created 2013/02/20 · arxiv updated 2013/02/21

Abstract

Consider an integral I(s):=∫₀^T e^-s(x2-icx)dx, where c>0 and T>0 are arbitrary positive constants. It is proved that I(s)∼ (i)/(sc) as s→ +∞. The asymptotic behavior of the integral J(s):=∫₀^Te^s(x2+icx)dx is also derived. One has J(s)∼ \frace^sT2+iscTs(2T+ic) as s→ +∞.

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