ASYMPTOTIC POWER SERIES EXPANSIONS OF INTEGRALS INVOLVING A LARGE PARAMETER. PART II: ONE SINGULARITY CLOSE TO THE SADDLE POINT
Abstract
The problem of a branch point or a pole close to a saddle point is considered. A convergent power series is developed for a particular class of integrals with one such singularity close to the saddle point and all other singularities far away. A set of necessary and sufficient conditions for the utility of this series is given and the series converges very rapidly if a particular parameter has large modulus. The special case for a first order pole is also given a separate treatment since the analysis can be made relatively simple for that case. The convergent series lead directly in all cases to more tractable semiconvergent ones although no presentation is made in the latter form. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1962
- Accession Number
- AD0292916
Entities
People
- John P. Ulrich
Organizations
- University of Wisconsin–Madison