I consider analyticity properties of scattering amplitude in higher dimensional field theories in the frame works of LSZ Axiomatic field theory. I prove existence of the Lehmann-Martin ellipse and prove generalized Jost-Lehmann-Dyson theorem
to achieve this goal. Here the basis for partial wave expansion is Gegenbaur
polynomial. I also prove analog of the Froissart-Martin bound for such theories.
J. Maharana, J. Math. Phys. (1917)