Regge Poles for Spinless Particles in the Backward Direction

A new Regge representation is introduced which involves Legendre functions of a modified argument. The analytic and asymptotic properties of the new partial waves are studied. It is shown that the new representation is valid in extended regions of the Mandelstam plane where the background integral converges. In these regions the new representation explicitly possesses the correct analyticity in the new plane corresponding to the ${cos\theta }_u$ plane. In regions of the Mandelstam plane where the conventional Regge representation is also valid, we can relate the new partial waves to the conventional Regge poles. The compatibility of our results with those of other groups is discussed.