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.
Publisher
Academia Romana Filiala Cluj
Reference18 articles.
1. R. Askey, Orthogonal Polynomial and Special Functions, Regional Conference Series in Applied Mathematics, SIAM Philadelphia, 1975.
2. A.A. Dovgoshei, Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane, Math. Zametki, 58(3) (1995), 355-364, https://doi.org/10.1007/BF02304768
3. R.P. Gilbert, Function Theoretic Methods in Partial Di?erential Equations, Math. in Science and Engineering, Vol. 54, Academic Press, New York, 1969.
4. G.M. Goluzin, Geometric Theory of Functions of one Complex Variable, Nauka, Moscow, 1966.
5. M. Harfaoui, Generalized order and best approximation of entire function in Lp-norm, Intern. J. Maths. Math. Sci., 2010 (2010), Article ID 360180, 1–15 https://doi.org/10.1155/2010/360180