mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-01 00:41:09 +00:00
1f03223571
This is an implementation of logarithmic series in Python. Reference: https://math.stackexchange.com/questions/3973429/what-is-a-logarithmic-series
49 lines
1.7 KiB
Python
49 lines
1.7 KiB
Python
"""
|
|
This is an implementation of logarithmic series in Python.
|
|
Reference: https://math.stackexchange.com/questions/3973429/what-is-a-logarithmic-series
|
|
"""
|
|
|
|
def logarithmic_series(x: float, n_terms: int = 5, expand: bool = False) -> list:
|
|
"""
|
|
Returns the logarithmic series for a number x (log x) upto n terms.
|
|
|
|
Parameters:
|
|
x: a floating point number for log(x)
|
|
n_terms: number of terms to be computed
|
|
expand: Set this flag to get the terms as real numbers, unset for unsolved expressions
|
|
|
|
Examples:
|
|
>>> logarithmic_series(3)
|
|
['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5']
|
|
|
|
>>> logarithmic_series(-3)
|
|
['-(4^1)/1', '(4^2)/2', '-(4^3)/3', '(4^4)/4', '-(4^5)/5']
|
|
|
|
>>> logarithmic_series(3, 10)
|
|
['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5', '-(2^6)/6', '(2^7)/7', '-(2^8)/8', '(2^9)/9', '-(2^10)/10']
|
|
|
|
>>> logarithmic_series(3, expand=True)
|
|
[2.0, -2.0, 2.6666666666666665, -4.0, 6.4]
|
|
"""
|
|
n_times_x_minus_1: float = x-1
|
|
n: int = 1
|
|
series: list = []
|
|
for _ in range(n_terms):
|
|
if (expand):
|
|
series.append(((-1)**(n+1))*(n_times_x_minus_1/n))
|
|
n_times_x_minus_1 *= (x-1)
|
|
else:
|
|
sign: str = '-' if (-1)**(n+1) == -1 else ''
|
|
term: str = sign+'('+str(x-1)+'^'+str(n)+')'+'/'+str(n)
|
|
if (term.startswith("-(-")):
|
|
term = '('+term[3::]
|
|
elif (term.startswith("(-")):
|
|
term = "-("+term[2::]
|
|
series.append(term)
|
|
n += 1
|
|
return series
|
|
|
|
if (__name__ == "__main__"):
|
|
import doctest
|
|
doctest.testmod()
|