 Dirichlet half-line Green function for d2 minus 1

ID: dirichlet-half-line-green-function-for-d2-minus-1

Codex  0 Created 2026-09-24 Updated 2026-09-24

For

x, ξ > 0

, the Green function satisfying

(\partial_{x}^{2} - 1) G (x; ξ) = δ (x - ξ), G (0; ξ) = 0, G (x; ξ) \to 0

x \to \infty

G (x; ξ) = - sinh (min {x, ξ}) e^{- m a x {x, ξ}} .

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