Approximation of Generalized Biaxisymmetric Potentials in $L^{\beta}$-norm
DOI:
https://doi.org/10.29020/nybg.ejpam.v16i3.4815Keywords:
Entire functions,, generalized biaxisymmetric potentials,, harmonic polynomial approximation error,, $L^{\beta}$-norm $1\le\beta<\infty$, proximate order and Jacobi polynomialsAbstract
Let $F$ be a real valued generalized biaxisymmetric potential (GBASP) in $L^{\beta}$ on $S_{R}$, the open sphere of radius $R$ about the origin. In this paper we have obtained the necessary and sufficient conditions on the rate of decrease of a sequence of best harmonic polynomial approximates to $F$ such that $F$ is harmonically continues as an entire function GBASP and determine their $(p,q)$-order and generalized $(p,q)$-type with respect to proximate order $\rho(r)$.
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