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Green function

One-dimensional modified Helmholtz Green function

For $x,\xi>0$, the <Green function> satisfying
$$
(\partial_x^2-1)G(x;\xi)=\delta(x-\xi),\qquad
G(0;\xi)=0,\qquad G(x;\xi)\to0
$$
as $x\to\infty$ is
$$
G(x;\xi)=-\sinh(\min\{x,\xi\})e^{-\max\{x,\xi\}}.
$$

Dirichlet half-line Green function for d2 minus 1

Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 3 / 5A / Solution

Dirichlet half-line Green function for d2 minus 1

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Dirichlet half-line Green function for d2 minus 1

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