Abstract: The paper deals with growth and approximation of solutions (not necessarily entire) of certain elliptic partial differential equations. These solutions are called Generalized Bi-axially Symmetric Potentials (GBSP's). The GBSP's are taken to be regular in a finite hyperball and influence of the growth of their maximum moduli on the rate of decay of their approximation errors in sup norm is studied. The authors obtain the characterizations of the q-type and lower q-type of a GBSP H ∈ H_R,0 < R < ∞, in terms of rate of decay of approximation error E_n(H,R₀), 0 < R₀ <R <∞.

Key words: Generalized bi-axially symmetric potentials, Elliptic partial differential equations, Index q, Entire GBSP polynomials, Sup norm