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maths/series/logarithmic_series.py
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@ -3,46 +3,49 @@ 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_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)
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::]
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__"):
if __name__ == "__main__":
import doctest
doctest.testmod()