Devendra Kumar, Growth Estimates of Entire Function Solutions of Generalized Bi-Axially Symmetric Helmholtz Equation, IJARM Volume 8, International Journal of Advanced Research in Mathematics (Volume 8)
https://www.scipress.com/IJARM.8.12
Abstract:
    Growth estimates for entire function solutions of the generalized bi-axially symmetric Helmholtz equation <i>∂</i><sup>2</sup><i>u</i>/<i>∂x</i><sup>2</sup> + <i>∂</i><sup>2</sup><i>u</i>/<i>∂y</i><sup>2</sup> + (2<i>µ</i>/<i>x</i>)·(∂<i>u</i>/∂<i>x</i>) + (2<i>ν</i>/<i>y</i>)·(∂<i>u</i>/∂<i>y</i>) +<i>k</i><sup>2</sup><i>u</i> = 0, (<i>µ</i>,<i>ν</i> Є R<sup>+</sup>), in terms of their Jacobi Bessel coefficients and ratio of these coefficients have been studied. Some relations for order and type also have been obtained in terms of Taylor and Neumann coefficients. Our results generalize and extend some results of Gilbert and Howard, McCoy, Kumar and Singh.
Keywords:
    Helmohltz Equation, Jacobi Bessel Coefficients, Order, Type