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

Devendra Kumar

doi:10.33993/jnaat471-1109

Authors

Devendra Kumar M.M.H.College, India

DOI:

https://doi.org/10.33993/jnaat471-1109

Keywords:

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

Abstract views: 224

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.

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