Theorems · Theorem · special functions
Polynomial.Chebyshev.C_two_mul_complex_cosh
∀ (θ : ℂ) (n : ℤ), Polynomial.eval (2 * Complex.cosh θ) (Polynomial.Chebyshev.C ℂ n) = 2 * Complex.cosh (↑n * θ)
The n-th rescaled Chebyshev polynomial of the first kind (Vieta–Lucas polynomial) evaluates on
2 * cosh θ to the value 2 * 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Complexstatement and proof · cited by 5,565
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.compproof · cited by 193
- Polynomial.eval_Xproof · cited by 172
- Polynomial.eval_Cproof · cited by 145
- Polynomial.eval_mulproof · cited by 127
- Complex.coshstatement and proof · cited by 118
- Polynomial.Chebyshev.Tproof · cited by 108
- inv_mul_cancel_left₀proof · cited by 47
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.C_two_mul_real_coshproof · cited by 0