New two-turning-point phase-integral formula for the residue of theSmatrix at a Regge pole

Abstract
An arbitrary-order phase-integral formula for the residue of the S matrix at a Regge pole is given. This formula is valid when there are two relevant transition zeros that may lie at an arbitrary distance from each other, possibly close together, but far away from all other transition points, the pole at the origin inclusive. It is also shown that the already-known phase-integral formula for the positions of the Regge poles is valid under the same general assumptions.