\(L^p\)-approximation and generalized growth of generalized biaxially symmetric potentials on hyper sphere

Abstract

The generalized order of growth and generalized type of an entire function \(F^{\alpha,\beta}\) (generalized biaxisymmetric potentials) have been obtained in terms of the sequence \(E_n^p(F^{\alpha,\beta},\Sigma_r^{\alpha,\beta})\) of best real biaxially symmetric harmonic polynomial approximation on open hyper sphere \(\Sigma_r^{\alpha,\beta}\). Moreover, the results of McCoy [8] have been extended for the cases of fast growth as well as slow growth.

Keywords

• Generalized order and type
• hyper sphere
• generalized biaxisymmetric polynomial approximation errors
• fast and slow growth
• Jacobi polynomial and Lp-norm