Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Roots of $ J_\gamma (z)\pm iJ_{\gamma +1}(z)=0$ and the evaluation of integrals with cylindrical function kernels

Authors: Srinivas Tadepalli and Costas Emmanuel Synolakis
Journal: Quart. Appl. Math. 52 (1994), 103-112
MSC: Primary 33C10
DOI: https://doi.org/10.1090/qam/1262322
MathSciNet review: MR1262322
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Abstract: An elementary proof is presented showing that the function $ f\left( z \right) = \\ {J_\gamma }\left( z \right) \pm i{J_{\gamma + 1}} \left( z \right)$, where $ \gamma $ is a natural number, has no zeroes in the lower and upper half-planes respectively. The roots of $ f\left( z \right)$ are given for certain values of $ \gamma $ and their locations are plotted. Cartesian maps (mappings of constant coordinate lines) of $ f\left( z \right)$ are obtained, and special features of these maps are discussed. Some integrals with cylindrical kernels involving $ f\left( z \right)$ are obtained in terms of the zeroes of $ {J_\gamma }\left( z \right)$.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/1262322
Article copyright: © Copyright 1994 American Mathematical Society

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