展开定理( Taylor) (要点) f(2)=∑an( f() an-21 (-a)n dc 逐项积分 ∴∫(z)= 2丌 (s-a)n+//(S)ds
Expansion in Taylor Series Taylor Expansion: Examples Identity Theorem for Analytic Functions Theorem (Taylor) Discussions & Remarks Illustrative Examples Ðm½n(Taylor) (:) f(z) = X∞ n=0 an(z − a) n an = 1 2π i I C f(ζ) (ζ − a) n+1 dζ = f (n) (a) n! ÅÈ© ∴ f(z) = 1 2π i I C "X ∞ n=0 (z − a) n (ζ − a) n+1# f(ζ)dζ = X ∞ n=0 1 2π i I C f(ζ) (ζ − a) n+1dζ (z − a) n C. S. Wu 1Ôù )Û¼êTaylorÐm
展开定理( Taylor) (要点) f(2)=∑an( f() an-21 (-a)n dc 逐项积分 ∴∫(z)= 2丌 76(=o)2+/(a ∑|2 f() d|(-a
Expansion in Taylor Series Taylor Expansion: Examples Identity Theorem for Analytic Functions Theorem (Taylor) Discussions & Remarks Illustrative Examples Ðm½n(Taylor) (:) f(z) = X∞ n=0 an(z − a) n an = 1 2π i I C f(ζ) (ζ − a) n+1 dζ = f (n) (a) n! ÅÈ© ∴ f(z) = 1 2π i I C "X ∞ n=0 (z − a) n (ζ − a) n+1# f(ζ)dζ = X ∞ n=0 1 2π i I C f(ζ) (ζ − a) n+1dζ (z − a) n C. S. Wu 1Ôù )Û¼êTaylorÐm
展开定理( Taylor) (要点) f(2)=∑an(2-a)y ∫() 2πiJe(-a)m ≈∫m(a) n f(2)=∑an(2-a) f(O C. S. Wu
Expansion in Taylor Series Taylor Expansion: Examples Identity Theorem for Analytic Functions Theorem (Taylor) Discussions & Remarks Illustrative Examples Ðm½n(Taylor) (:) f(z) = X∞ n=0 an(z − a) n an = 1 2π i I C f(ζ) (ζ − a) n+1 dζ = f (n) (a) n! ∴ f(z) = X ∞ n=0 an(z − a) n an = 1 2π i I C f(ζ) (ζ − a) n+1dζ = f (n) (a) n! C. S. Wu 1Ôù )Û¼êTaylorÐm
展开定理( Taylor) (要点) f(2)=∑an(2-a)y ∫() 2πiJe(-a)m ≈∫m(a) n f(2)=∑an(2-a) =0 f() ZLI C. S. Wu
Expansion in Taylor Series Taylor Expansion: Examples Identity Theorem for Analytic Functions Theorem (Taylor) Discussions & Remarks Illustrative Examples Ðm½n(Taylor) (:) f(z) = X∞ n=0 an(z − a) n an = 1 2π i I C f(ζ) (ζ − a) n+1 dζ = f (n) (a) n! ∴ f(z) = X ∞ n=0 an(z − a) n an = 1 2π i I C f(ζ) (ζ − a) n+1dζ = f (n) (a) n! C. S. Wu 1Ôù )Û¼êTaylorÐm
展开定理( Taylor) (要点) f(2)=∑an(2-a)y ∫() 2πiJe(-a)m ≈∫m(a) n f(2)=∑an(2-a) =0 f() 2π1JC C. S. Wu
Expansion in Taylor Series Taylor Expansion: Examples Identity Theorem for Analytic Functions Theorem (Taylor) Discussions & Remarks Illustrative Examples Ðm½n(Taylor) (:) f(z) = X∞ n=0 an(z − a) n an = 1 2π i I C f(ζ) (ζ − a) n+1 dζ = f (n) (a) n! ∴ f(z) = X ∞ n=0 an(z − a) n an = 1 2π i I C f(ζ) (ζ − a) n+1dζ = f (n) (a) n! C. S. Wu 1Ôù )Û¼êTaylorÐm