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- W814152507 abstract "An overview is given for the Dirichlet-to-Neumann map for outgoing solutions to the “radial wave equation” in the context of nonreflecting radiation boundary conditions on a spherical domain. We then consider the Macdonald function Kl+1/2(z) for l ∈ Z≥0, a solution to the half-integer order modified Bessel equation. This function can be expressed as Kl+1/2(z) = √ π 2z ezpl(z), where pl(z) is a degree-l monic polynomial with simple roots in the left-half plane. By exploiting radiation boundary conditions for the “radial wave equation”, we show that the root set of pl(z) also obeys l additional polynomial constraints. These constraints are in fact Newton’s identities which relate a polynomial’s coefficients to the power sums of its roots. We follow this with numerical verification up to order l = 20." @default.
- W814152507 created "2016-06-24" @default.
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- W814152507 date "2014-09-12" @default.
- W814152507 modified "2023-09-26" @default.
- W814152507 title "On Roots of the Macdonald Function" @default.
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- W814152507 hasPublicationYear "2014" @default.
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