Measures of Growth of Entire Solutions of Generalized Axially Symmetric Helmholtz Equation. (3rd January 2013) - Kumar, Devendra; Singh, Rajbir
Abstract : For an entire solution of the generalized axially symmetric Helmholtz equation ∂ 2 u / ∂ x 2 + ∂ 2 u / ∂ y 2 + ( 2 μ / y ) ( ∂ u / ∂ y ) + k 2 u = 0,   μ > 0, measures of growth such as lower order and lower type are obtained in terms of the Bessel-Gegenbauer coefficients. Alternative characterizations for order and type are also obtained in terms of the ratios of these successive coefficients.