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pre-commit-ci[bot] 2024-10-23 19:36:43 +00:00
parent 1f03223571
commit 469f0fc4ec
1 changed files with 19 additions and 16 deletions
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maths/series/logarithmic_series.py
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@ -3,6 +3,7 @@ This is an implementation of logarithmic series in Python.
Reference: https://math.stackexchange.com/questions/3973429/what-is-a-logarithmic-series 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: 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. Returns the logarithmic series for a number x (log x) upto n terms.
@ -29,20 +30,22 @@ def logarithmic_series(x: float, n_terms: int = 5, expand: bool = False) -> list
n: int = 1 n: int = 1
series: list = [] series: list = []
for _ in range(n_terms): for _ in range(n_terms):
if (expand): if expand:
series.append(((-1) ** (n + 1)) * (n_times_x_minus_1 / n)) series.append(((-1) ** (n + 1)) * (n_times_x_minus_1 / n))
n_times_x_minus_1 *= (x-1) n_times_x_minus_1 *= x - 1
else: else:
sign: str = '-' if (-1)**(n+1) == -1 else '' sign: str = "-" if (-1) ** (n + 1) == -1 else ""
term: str = sign+'('+str(x-1)+'^'+str(n)+')'+'/'+str(n) term: str = sign + "(" + str(x - 1) + "^" + str(n) + ")" + "/" + str(n)
if (term.startswith("-(-")): if term.startswith("-(-"):
term = '('+term[3::] term = "(" + term[3::]
elif (term.startswith("(-")): elif term.startswith("(-"):
term = "-(" + term[2::] term = "-(" + term[2::]
series.append(term) series.append(term)
n += 1 n += 1
return series return series
if (__name__ == "__main__"):
if __name__ == "__main__":
import doctest import doctest
doctest.testmod() doctest.testmod()