Share-Based Compensation (Compensation Cost Recognized in Income Statement) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Share-Based Payment Arrangement [Abstract]
Before-tax share-based compensation cost	$ 60.7	$ 49.5	$ 44.5
Income tax benefit	(14.6)	(12.1)	(11.0)
After-tax share-based compensation cost	$ 46.1	$ 37.4	$ 33.5