Create logarithmic_series.py

maths/series/logarithmic_series.py

@@ -0,0 +1,54 @@
+"""
+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_value: float, n_terms: int = 5, expand: bool = False) -> list:
+    """
+    Returns the logarithmic series for a number x (log x) upto n terms.
+
+    Parameters:
+        x_value: 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, 6)
+        ['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5', '-(2^6)/6']
+
+        >>> logarithmic_series(3, expand=True)
+        [2.0, -2.0, 2.6666666666666665, -4.0, 6.4]
+    """
+    n_times_x_minus_1: float = x_value - 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_value - 1
+        else:
+            sign: str = "-" if (-1) ** (n + 1) == -1 else ""
+            term: str = (
+                sign + "(" + str(x_value - 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()