Theorems · Definition · real analysis
Real.sqrtTwoAddSeries
ℝ → ℕ → ℝ
the series sqrtTwoAddSeries x n is sqrt(2 + sqrt(2 + ... )) with n square roots,
starting with x. We define it here because cos (pi / 2 ^ (n+1)) = sqrtTwoAddSeries 0 n / 2
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
Cited by19
Results whose statement or proof uses this declaration.
- Real.sin_pi_over_two_pow_succstatement and proof · cited by 6
- Real.pi_lower_bound_startstatement and proof · cited by 5
- Real.sqrtTwoAddSeries_step_downstatement and proof · cited by 5
- Real.pi_upper_bound_startstatement and proof · cited by 5
- Real.sqrtTwoAddSeries_step_upstatement and proof · cited by 5
- Real.cos_pi_over_two_powstatement · cited by 5
- Real.sqrtTwoAddSeries_monotone_leftstatement · cited by 2
- Real.sqrtTwoAddSeries_succstatement · cited by 2
- Real.pi_gt_sqrtTwoAddSeriesstatement and proof · cited by 1
- Real.pi_lt_sqrtTwoAddSeriesstatement and proof · cited by 1
- Real.sqrtTwoAddSeries_lt_twostatement · cited by 1
- Real.sqrtTwoAddSeries_zero_nonnegstatement and proof · cited by 1