FlintCooksonHills.lean`

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 2 contain sorry, 0 declared as axioms

Convergence of the Flint Hills and Cookson Hills series

References:

Imports (1)

FormalConjecturesUtil

theorem FlintCooksonHills.flint_hills_series_converges The Flint Hills series summing $csc(n)^2 / n^3$ from $n=1$ to $\infty$ converges sorry line 39 source
Source documentation
The Flint Hills series summing $csc(n)^2 / n^3$ from $n=1$ to $\infty$ converges. (Note that we 0-index the series below.)

depends on sorry what this means
Statement uses: Iff, True, Summable, Real, Nat, HDiv.hDiv, OfNat.ofNat, HMul.hMul, HPow.hPow, HAdd.hAdd, Real.sin, SummationFilter.unconditional
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
40 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem flint_hills_series_converges :
    answer(sorry) ↔
      Summable (fun n : ℕ =>
        1 / ((((n + 1) : ℝ)^3) * (Real.sin (n + 1)^2))) := by
…
```
theorem FlintCooksonHills.cookson_hills_series_converges The Cookson Hills series summing $sec(n)^2 / n^3$ from $n=1$ to $\infty$ converges sorry line 49 source
Source documentation
The Cookson Hills series summing $sec(n)^2 / n^3$ from $n=1$ to $\infty$ converges.

depends on sorry what this means
Statement uses: Iff, True, Summable, Real, Nat, HDiv.hDiv, OfNat.ofNat, HMul.hMul, HPow.hPow, HAdd.hAdd, Real.cos, SummationFilter.unconditional
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
40 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem cookson_hills_series_converges :
    answer(sorry) ↔
      Summable (fun n : ℕ =>
        1 / ((((n + 1) : ℝ)^3) * (Real.cos (n + 1)^2))) := by
…
```