P. Vaudon et B. Jecko, A GENERAL FORMULATION FOR ASYMPTOTIC EXPANSIONS WITH A POLE NEAR THE SADDLE-POINT, Annales des telecommunications, 50(7-8), 1995, pp. 686-694
We describe the two uniform asymptotic expansions which already exist
and which are commonly used in asymptotic electromagnetic theories, wh
en a pole approaches the saddle point. Then, we establish a simple rel
ation between these two expansions. By analyzing this relation, we giv
e the general form of any asymptotic expansion with a pole near the sa
ddle point. By using diffraction integrals, we give explicit examples
and compare the corresponding numerical computations. Then we conclude
by examining the specific problem of many coalescing poles singularit
ies.