






def      __lowercase					( snake_case ):







				"""simple docstring"""






				if length <= 0 or not isinstance(snake_case,  snake_case ):
								raise ValueError('''Length must be a positive integer.''' )
				return [n * (2 * n - 1) for n in range(snake_case )]


if __name__ == "__main__":
					print(hexagonal_numbers(length=5))
					print(hexagonal_numbers(length=10))














from __future__ import annotations

from math import pi, sqrt

def      __lowercase					( snake_case,  snake_case ):







				"""simple docstring"""






				if inductance <= 0:
								raise ValueError('''Inductance cannot be 0 or negative''' )

				elif capacitance <= 0:
								raise ValueError('''Capacitance cannot be 0 or negative''' )

				else:
								return (
								    "Resonant frequency",
								    float(1 / (2 * pi * (sqrt(inductance * capacitance ))) ),
								)


if __name__ == "__main__":
					import doctest

					doctest.testmod()






