Create logarithmic_series.py

This is an implementation of logarithmic series in Python.
Reference: https://math.stackexchange.com/questions/3973429/what-is-a-logarithmic-series

maths/series/logarithmic_series.py

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+"""
+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()