Share-Based Compensation (Compensation Cost Recognized in Income Statement) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Share-Based Payment Arrangement [Abstract]
Before-tax share-based compensation cost	$ 61.7	$ 60.7	$ 49.5
Income tax benefit	(14.9)	(14.6)	(12.1)
After-tax share-based compensation cost	$ 46.8	$ 46.1	$ 37.4