Accession Number:

AD0292997

Title:

ASYMPTOTIC POWER SERIES EXPANSIONS OF INTEGRALS INVOLVING A LARGE PARAMETER. PART I. LARGE SEPARATION OF ALL SINGULARITIES FROM THE SADDLE POINT

Descriptive Note:

Corporate Author:

WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1962-10-01

Pagination or Media Count:

1.0

Abstract:

A BRIEF REVIEW OF METHODS USED TO OBTAIN ASYMPTOTIC POWER SERIES EXPANSIONS FOR CONTOUR INTEGRALS INV LVING A LARGE PARAMETER IS PRESENTED AND CRITICISM OF THESE METHODS IS GIVEN. An approach is then developed which produces a convergent series with a bounded remainder error for a particular class of such functions. These functions depend upon three parameters a set of conditions involving the relative ranges of these parameters is given which is necessary and sufficient to the remainder being acceptably small. The new development leans heavily on full utilization of the region about the saddle point in which the integrand is analytic. The usual semiconvergent asymptotic power series expansion is derived from the new results as a special case. Author

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE