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In this paper we study the growth and  L  δ -approximation, 1 ≤ δ ≤ ∞, of solutions (not necessarily entire) of Helmholtz-type equations. Moreover, we obtain the characterization of order and type of  H  ∈  H R  , 0 &lt;  R  &lt; ∞, in terms of decay of approximation errors  E n  ( H , R  0 ) andE   n  ,  δ   i    (  H  ,   R  0   )$E^{i}_{n,\delta } (H,R_0)$   ,  i  = 1,2. Our results extend and improve the results obtained by McCoy [J. Approx. Theory 25 (1979), 153–168].

Growth and L δ -approximation of solutions of the Helmholtz equation in a finite disk