Near a, an infinitely differentiable f is represented by Σ f^(n)(a)(x-a)^n/n!, when the series converges to f. Power-series expansion of analytic functions.
Taylor series
Related concepts
- Derivative
- Series convergence
- Σ z₁ʲz₂ᵏ/4^{j+k} = 16/((z₁-4)(z₂-4)); pins at (1,1), (0,2)
- Chebyshev polynomials T_n: orthogonal basis + minimax optimality
- Bernstein polynomials B_{k,n}(x): partition of unity + Weierstrass proof
- Padé approximant [m/n]: rational P_m/Q_n matching Taylor to order m+n
- [1/1] Padé of exp: (1+x/2)/(1-x/2); leading O(x³) residual 1/12
- Creutz ratio: χ(R,T) = -log[W(R,T)·W(R-1,T-1)/(W(R-1,T)·W(R,T-1))] → σ·a²
- Kerr-lens mode-locking: self-focusing via n₂·I in Ti:sapphire
- CCSD(T) gold standard
- Pitzer model of electrolyte activity