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physics/gamma_function.py

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+"""
+Gamma function is a very useful tool in physics.
+It helps calculating complex integral in a convenient way.
+for more info: https://en.wikipedia.org/wiki/Gamma_function
+"""
+
+# Importing packages
+from math import sqrt, pi
+from re import match
+from typing import Union
+
+
+def gamma(num : Union[int, float]) -> Union[int, float]:
+    """
+    Calculates the value of Gamma function of num
+    where num is either an integer (1,2,3..) or a half-integer (0.5,1.5,2.5...).
+    Implemented using recursion
+    Examples:
+    >>> Gamma of: 0.5
+    √π
+    >>> Gamma of: 2
+    1
+    >>> Gamma of: 3.5
+    1.875√π
+    """
+    if num == 1:
+        return 1
+    elif num == 0.5:
+        return sqrt(pi)
+    elif num > 1:
+        return (num - 1) * gamma(num - 1)
+    else:
+        # Error
+        return -2
+
+
+def test_gamma() -> None:
+    """
+    >>> test_gamma()
+    """
+    assert sqrt(pi) == gamma(0.5)
+    assert 1 == gamma(1)
+    assert 1 == gamma(2)
+
+
+if __name__ == "__main__":
+    # Initialize boolean
+    number = True
+    # Get input from user
+    input_ = input("Gamma of: ")
+    # Ensure valid input
+    try:
+        # Ensure input matches half-integer (float) pattern
+        if match(r'^[0-9]*\.5$', input_):
+            # Convert string to float
+            num = float(input_)
+        # Ensure input matches an integer pattern
+        elif match(r'^[1-9][0-9]*$', input_):
+            # Convert string to int
+            num = int(input_)
+        # Input is not a valid number
+        else:
+            # raise an error
+            raise ValueError
+    # Ensure print an error message
+    except ValueError:
+        print("Invalid input: Must be an integer or an half-integer!")
+        number = False
+    finally:
+        # Ensure input is a valid number
+        if number:
+            # Ensure input is an integer
+            if (isinstance(gamma(num), int)):
+                # Print result
+                print(gamma(num))
+            # Otherwise print results with √π (gamma of 0.5 is √π)
+            # Therefore all results will be a number times √π
+            else:
+                results = "{result:.4f}".format(result=gamma(num) / sqrt(pi))
+                results = results.rstrip('0').rstrip('.')
+                if results == "1":
+                    results = ""
+                print(results + "\u221A\u03c0")