Is there a way to calculate the half range Fourier series in SymPy?-CodePudding

For example, if I want the Fourier series of the function f(x) = x(π-x) on [0, π], I can calculate the coefficients of the sine series:

which works by considering f(x) in a

CodePudding user response：

Yes, it is possible to calculate the half-range Fourier series in SymPy. You can use the fourier_series function in the sympy.functions.special.orthogonal module to calculate the half-range Fourier series of a function. The function takes the function to be expanded, the variable to expand with respect to, the lower and upper limits of the expansion interval, and the number of terms in the expansion as arguments.

Here is an example of how to use the fourier_series function to calculate the half-range Fourier series of a function:

from sympy.functions.special.orthogonal import fourier_series
from sympy import pi, Symbol
x = Symbol('x')
f = x**2
a = -pi
b = pi
n = 5
fourier_series(f, (x, a, b), n)

This will give you a sum of the first 5 terms of the half range Fourier series of f(x) = x^2, where the interval of expansion is [-pi,pi].