Publisher : Eliza Parker
Taylor polynomial
series
derives from the function's derivatives at a single point.f(z)
about a point z = a
is given by :f(z) = f(a) + f'(a)*(z-a) + f''(a)*(z-a) ^2/2! + f'''(a)*(z-a) ^3/3! + ...
f'(a), f’’(a), f'''(a), ...
represent the 1st, 2nd, 3rd, and higher derivatives of f(z)
calculated at z=a
, and the symbol n!
denotes the factorial of n.a
”, with the residue term Rn(z)
assumed as:f(z) = f(a) + f'(a)*(z-a)/1! + f''(a)*(z-a)2/2! + ... + fn(a)*(z-a) n/n! + Rn(z)
Rn(z)
is the residue period, which is the same as the nth-derivative
of f(z) calculated at particular point c between “a
” and “z”, multiplied by the (z-c)(n+1)
divided by (n+1)!
which is Rn(z) = [f(n+1) (c)*(z-c) (n+1)] / (n+1)!
f(n)(z)
symbolizes the nth
derivative of f(z)
concerning z.f(z) = sin(z)
centered at z=0
:z=a
is :f(z) = f(a) + f'(a)*(z-a)/1! + f''(a)*(z-a) ^2/2! + f'''(a)*(z-a) ^3/3! + ...
f', f'', f’’’
, represent the 1st, 2nd, 3rd, etc. differentiation of f(z)
, correspondingly.Taylor series calculator
to get rid of lengthy and time-consuming calculations.