Income Taxes - Narrative (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Income Tax Disclosure [Abstract]
Tax benefit attributable to non-U.S. government sponsored tax incentive programs	$ 61.2	$ 59.1	$ 55.1
Tax benefit per diluted share attributable to non-U.S. government sponsored tax incentive programs (in usd per share)	$ 0.52	$ 0.51	$ 0.46
Gross unrecognized tax benefits	$ 4.3	$ 25.5	$ 19.9	$ 20.1
Accrued interest and penalties for unrecognized tax benefits	1.5	4.0
Benefits (expense) recognized for interest and penalties related to unrecognized tax benefits	2.5	(0.7)	$ (0.8)
Reasonably possible amount of reduction of gross unrecognized tax benefit in the next twelve months	4.2
Reasonably possible amount of net reduction to income tax provision in the next twelve months if unrecognized tax benefits were recognized, including the recognition of interest and penalties and offsetting tax assets	5.7
Transition tax expense (benefit)	$ 264.8	$ 296.0