On a Formula of Inversion
Copyright policy )On a Formula of Inversion
This paper develops a formula of inversion for an integral transform of a type similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann function $Y_u (kr)$ and the variable r varies over the truncated infinite interval $a \leq r 0$. The transform is useful in the investigation of functions that satisfy the Helmholtz equation and a condition of radiation at infinity.
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, inversion formula, Transform methods (e.g., integral transforms) applied to PDEs, Neumann type Bessel function, Special integral transforms (Legendre, Hilbert, etc.), Helmholtz equation, radiation condition
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, inversion formula, Transform methods (e.g., integral transforms) applied to PDEs, Neumann type Bessel function, Special integral transforms (Legendre, Hilbert, etc.), Helmholtz equation, radiation condition
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