Theorems · Theorem · special functions
Polynomial.Chebyshev.T_real_cosh
∀ (θ : ℝ) (n : ℤ), Polynomial.eval (Real.cosh θ) (Polynomial.Chebyshev.T ℝ n) = Real.cosh (↑n * θ)
The n-th Chebyshev polynomial of the first kind evaluates on cosh θ to the
value cosh (n * θ).
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Complexproof · cited by 5,565
- Complex.ofRealproof · cited by 1,654
- Polynomial.evalstatement and proof · cited by 796
- Real.coshstatement and proof · cited by 119
- Complex.coshproof · cited by 118
- Polynomial.Chebyshev.Tstatement and proof · cited by 108
- Polynomial.Chebyshev.T_complex_coshproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.one_lt_eval_T_realproof · cited by 2