Growth estimates for entire function solutions of the generalized bi-axially symmetric Helmholtz equation *∂*^{2}*u*/*∂x*^{2} + *∂*^{2}*u*/*∂y*^{2} + (2*µ*/*x*)·(∂*u*/∂*x*) + (2*ν*/*y*)·(∂*u*/∂*y*) +*k*^{2}*u* = 0, (*µ*,*ν* Є R^{+}), 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.

Periodical:

International Journal of Advanced Research in Mathematics (Volume 8)

Pages:

12-26

Citation:

D. Kumar, "Growth Estimates of Entire Function Solutions of Generalized Bi-Axially Symmetric Helmholtz Equation", International Journal of Advanced Research in Mathematics, Vol. 8, pp. 12-26, 2017

Online since:

April 2017

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Open Access

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Creative Commons Attribution 4.0 International License

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[1] D. Dinh, " $$\varvec{(m,h)}$$ ( m , h ) -Monogenic Functions Related to Axially Symmetric Helmholtz Equations", Advances in Applied Clifford Algebras, Vol. 29, 2019

DOI: https://doi.org/10.1007/s00006-019-1023-7