A technique recently developed for inelastic electron proton scattering is applied for inelastic electron pion scattering. It is found that all the derivatives of off-shell form factor of pion nears=m_π² and for largeQ² are bounded from above, provided that the dispersion relation for the form factor requires no more than one subtraction. The elastic pion form factor is bounded by [lnQ²]^c/Q², wherec is any positive constant.

Using unitarity, analyticity and the hypothesis of Bjorken scaling inequalities have been derived for the upper bounds on the wave function renormalization constant of pion.

A phenomenological representation for differential cross-section recently proposed using Mandelstam analyticity and convergent polynomial expansion (CPE) which has been found to be successful in describing scaling of the differential cross-section-ratio data for several elastic diffractive and inelastic nondiffractive processes is used to analyse the energy dependence of the slope-parameter data at high energies, extrapolate the slope parameter and predict the differential cross-section ratio as a function of |t| at higher energies forπ^±pndK⁺p scattering. Following the method of Hansen and Krisch it is found that, in spite of the existence of rather widely varying data points for nearbys values, a more systematic trend in the energy dependence of the slope parameter emerges when a statistical average of the existing high-energy data is used. Extrapolating the fits to the average data ontos → ∞ provides strong evidence in favour of a model-independent result that asymptotically theπ^±p slopes may be equal. There is also a strong indication to the effect that each of these two slopes may be equal to theK⁺p slope fors → ∞. Using the scaling curves generated by the existing data on differential cross-section ratio and extrapolated values of the slope parameter, the differential cross-section ratio for each of the three processes is predicted as a function of |t| for higher energies.

Existing data on the differential cross-section ratio at high energies for pp,$$\bar p$$p, π^±p andK^±p scatering have been fitted by the proposed convergent polynomial expansion to determine the unknown coefficients in the scaling function. It is found that the data are very well represented within and somewhat outside the peak regions by only four or five terms in the proposed series in terms of Laguerre polynomials.