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Manuscript I-B-VP@3 · I-B-VP-v3.tex · section · 93c04eb4

Euclidean kernels, diffraction, and local Hadamard form

Euclidean kernels, diffraction, and local Hadamard form · lines 696–706

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For Euclidean points set

cosh η = \frac{r ^{2} + r ^{'2} + Δ τ ^{2} + Δ z ^{2}}{2 r r ^{'}}, σ_{E}^{2} = r^{2} + r^{'2} - 2 r r^{'} cos ϑ + Δ τ^{2} + Δ z^{2} .

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$cosh η = \frac{r ^{2} + r ^{'2} + Δ τ ^{2} + Δ z ^{2}}{2 r r ^{'}}, σ_{E}^{2} = r^{2} + r^{'2} - 2 r r^{'} cos ϑ + Δ τ^{2} + Δ z^{2} .$

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proposition: Proposition: Euclidean mode sum