What is the Taylor Series expansion for f(x+2h)?
February 20th, 2023
Let 2h = a,
##f(x+2h) = f(x+a)##
Taylor series of this is:
##f(x+a) = f(x) + f'(x)*a+ f”(x)*a^2/(2!) + f”'(x)*a^3/(3!) + ….##
##f(x+a) = sum_(n=0)^∞f^(n)(x)*a^n/(n!)##
Substitute a = 2h,
##f(x+a) = sum_(n=0)^∞f^(n)(x)*(2h)^n/(n!)##
To note : ##f^(n)(x)## means the ##n^(th)## differential of f(x). Also the function f(x) has to be infinitely differentiable.