411 REFERENCE · Wikibooks
On 2D Inverse Problems/Echo
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
The response could be echo [ˈɛkəʊ],
φψ = +1 φψ = -1
(ζ-world) (η-world)
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RECURSION: R_m = cot·(x-1/x)+back R_m = ±cot·(x-1/x)+back
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| (1-(-1)^m) twist |
|←—————————————————————————|
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SEQUENCES: x^m - x^{-m} x^m - (-1)^m x^{-m}
(all same sign) (alternating signs)
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TRIG FORM: 2i·sin(mθ) sin(mθ) + i·(1-(-1)^m)·...
(x=e^iθ) 2·cos(mθ) cos(mθ)·(1+(-1)^m)/2 + ...
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DIRICHLET ζ(s) = Σ 1/n^s η(s) = Σ (-1)^{n-1}/n^s
SERIES: | |
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|——— η(s) = (1-2^{1-s})ζ(s) ——|
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OPERATOR: (-Δ) √(-Δ)
(full Laplacian) (half-derivative)
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SELF-DUALITY: Z·Z* = +1 Z·Z* = -1
(unitary/lossless) (Fibonacci/golden)
the geometry of electricity:
±±±±±±±±±±±±±...
x^(m+1)-1/(±x)^(m+1) x^m±1/x^m x^(m-1)-1/(±x)^(m-1)
-------------------- = ---------(x-1/x) + --------------------.
x^m-1/(±x)^m x^m-1/x^m x^m-1/(±x)^m
≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠≠