Updated file

maths/gamma_recursive.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)
+ # 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("Error: Input must be an integer or an half-integer!")
+ number = False
+ finally:
+ # Ensure input is a valid number
+ if number:
+ print(f"\u0393({num}) = ", end="")
+ # 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 = f"{gamma(num) / sqrt(pi):.4f}"
+ results = results.rstrip("0").rstrip(".")
+ if results == "1":
+ results = ""
+ print(results + "\u221A\u03c0")