○ Taylor Series
｢f(x)▽ⁿx｢a｣/n!·(x−a)˄n Σn=0,∞｣
○ Maclaurin Series
｢f(x)▽ⁿx｢0｣/n!·x˄n Σn=0,∞｣
┅
f(x)▽⁰x
= c₀·(x−a)˄0
+ c₁·(x−a)˄1
+ c₂·(x−a)˄2
+ c₃·(x−a)˄3 + ...
= ｢cₙ·(x−a)˄n Σn=0,∞｣
f(x)▽⁰x｢a｣ = c₀ = c₀·0!
c₀ = f(x)▽⁰x｢a｣/0!
f(x)▽¹x
= c₁·1·(x−a)˄0
+ c₂·2·(x−a)˄1
+ c₃·3·(x−a)˄2
+ c₄·4·(x−a)˄3 + ...
= ｢cₙ·n·(x−a)˄(n−1) Σn=1,∞｣
f(x)▽¹｢a｣ = c₁·1 = c₁·1!
c₁ = f(x)▽¹｢a｣/1!
f(x)▽²x
= c₂·2·1·(x−a)˄0
+ c₃·3·2·(x−a)˄1
+ c₄·4·3·(x−a)˄2
+ c₅·5·4·(x−a)˄3 + ...
= ｢cₙ·n·(n−1)·(x−a)˄(n−2) Σn=2,∞｣
f(x)▽²x｢a｣ = c₂·2·1 = c₂·2!
c₂ = f(x)▽²x｢a｣/2!
f(x)▽³x
= c₃·3·2·1·(x−a)˄0
+ c₄·4·3·2·(x−a)˄1
+ c₅·5·4·3·(x−a)˄2
+ c₆·6·5·4·(x−a)˄3 + ...
= ｢cₙ·n·(n−1)·(n−2)·(x−a)˄(n−3) Σn=3,∞｣
f(x)▽³x｢a｣ = c₃·3·2·1 = c₃·3!
c₃ = f(x)▽³x｢a｣/3!
┅
Taylor Series
｢f(x)▽ⁿx｢a｣/n!·(x−a)˄n Σn=0,∞｣
Maclaurin Series
｢f(x)▽ⁿx｢0｣/n!·(x−0)˄n Σn=0,∞｣
= ｢f(x)▽ⁿx｢0｣/n!·x˄n Σn=0,∞｣
