On the generalized growth and approximation of entire solutions of certain elliptic partial differential equation

Abstract

For an entire function solution of generalized bi-axisymmetric potential equation, we obtain a relationship between the generalized growth characteristics and polynomial approximation errors in sup norm by using the general functions introduced by Seremeta [On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion, Amer. Math. Soc. Transl. 88 (1970), no. 2, 291–301].

Keywords

• entire gbsps functions
• gbsps polynomial approximation error
• generalized order and type
• jacobi polynomials and sup norm
• 41a15
• 30b10