Exactifying the Hankel integral Poincaré asymptotic expansion by the distributional method and the role of rearrangement in the accuracy of the exactified expansion
We use the distributional approach to determine the asymptotic expansion of the Hankel integral ∫0∞ Φ(x) x–λ Jν(bx) dx for arbitrarily large b. We find that the approach reproduces the known Poincaré asymptotic expansion plus the exactifying terms that are missed out by the Poincaré expansion. It is demonstrated that exactifying the Poincaré expansion does not necessarily produce an expansion that is superior to the Poincaré expansion in numerically approximating the Hankel integral. However, it is also demonstrated that a rearrangement of the exactified expansion may lead to an expansion that is more accurate than the Poincaré asymptotic expansion.
By submitting their manuscript to the Samahang Pisika ng Pilipinas (SPP) for consideration, the Authors warrant that their work is original, does not infringe on existing copyrights, and is not under active consideration for publication elsewhere.
Upon acceptance of their manuscript, the Authors further agree to grant SPP the non-exclusive, worldwide, and royalty-free rights to record, edit, copy, reproduce, publish, distribute, and use all or part of the manuscript for any purpose, in any media now existing or developed in the future, either individually or as part of a collection.
All other associated economic and moral rights as granted by the Intellectual Property Code of the Philippines are maintained by the Authors.