 Laguerre contour-integral amplitude

ID: laguerre-contour-integral-amplitude

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Laguerre contour-integral amplitude by

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

For the Laguerre equation

z y^{''} + (1 - z) y^{'} + λ y = 0,

y = \int_{γ} e^{z t} f (t) d t

gives

f (t) = t^{- λ - 1} (t - 1)^{λ} .

The contour must make the endpoint contribution

[e^{z t} t^{- λ} (t - 1)^{λ + 1}]_{\partial γ}

vanish.

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