Slow Growth and Approximation of Entire Solution of Generalized Axially Symmetric Helmholtz Equation

The Chebyshev polynomial approximation of an entire solution of Generalized Axially Symmetric Helmholtz Equation (GASHE) in Banach spaces B(p,q,m) space, Hardy space and Bergman space) have been studied. Some bounds on generalized order of GASHE functions of slow growth have been obtained in terms of the Bessel-Gegenbauer coefficients and approximation errors using function theoretic methods.