From the singularity structure of a form factor $G\left(t\right)\mathrm{}$ and that of the imaginary part $F(s,t)\mathrm{}$ of a scattering amplitude, in the $t$ plane, and from certain assumptions on their growth outside the physical region, we obtain representations of $G\left(t\right)\mathrm{}$ and $F(s,t)\mathrm{}$ from which we deduce an asymptotic form of these functions. It is shown that the imaginary part of the scattering amplitude for identical particles has the same analytical structure in the ${P_t}^2$ plane (square of the transverse momentum) as $G\left(t\right)\mathrm{}$ in the $t$ plane, and they have the same asymptotic behavior in the variables ${P_t}^2$ and $t$, respectively. For the former case, we also obtain an exact representation of $\ln F(s,t)\mathrm{}$ as a power series in trigonometric functions with coefficients which are functions of $s$. These coefficients can, in principle, be determined from experiment by a procedure similar to that employed in partial-wave analysis. It is argued that a few terms in this series would suffice for a parametrization of the scattering amplitude at all angles and energies. The representations of $G\left(t\right)\mathrm{}$ and $F(s,t)\mathrm{}$ are also used to obtain asymptotic lower bounds on the form factors and the scattering amplitudes similar to those previously obtained by Martin. For the scattering amplitude, we have obtained bounds separately for identical and nonidentical particles, and in the latter case our bound is well behaved at $\theta ={90}^{\circ }$, unlike that of Martin.

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