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Address review comments: fix attribution, notebook-verbatim Möbius sum, add Fourier convention
Co-authored-by: blackboxprogramming <118287761+blackboxprogramming@users.noreply.github.com>
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@@ -1,7 +1,7 @@
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# Notebook Page 1 — Transcription
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> Source: `→ halting problem.pdf`, page 1 of 24.
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> Transcribed by Alexa Louise Amundson.
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> Author: Alexa Louise Amundson. Markdown transcription by repository maintainers.
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---
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@@ -102,7 +102,7 @@ M(x) = Σ_{n ≤ x} μ(n)
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```
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Σ_{n=1}^{∞} μ(n)/n = 0
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Σ_{n=1}^{∞} (μ(n) ln n)/n = −1
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Σ_{n=1}^{∞} μ(n)/n² = 6/π² = 1/ζ(2)
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Σ_{n=1}^{∞} μ(n)/n² = 15/π² [as written in notebook; correct value is 6/π² = 1/ζ(2)]
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```
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> **Historical note:** Gauss considered the Möbius function over 30 years before Möbius,
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@@ -132,6 +132,11 @@ f(x) = a · e^(−(x−b)² / 2c²)
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### Fourier Transform Proofs
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Convention used (unitary, angular frequency):
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```
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F{ f(x) }(ω) = ∫_{−∞}^{∞} f(x) e^{−iωx} dx
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```
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**Transform of a Gaussian:**
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```
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F{ a · e^(−bx²) } = (a / √(2b)) · e^(−ω² / 4b)
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