Income Taxes - Narrative (Details) - USD ($)	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Income Tax Disclosure [Abstract]
Income tax liabilities	$ 233,700,000	$ 264,800,000
Income tax paid	31,200,000	31,200,000	$ 28,700,000
Effective income tax rate reconciliation, change in deferred tax assets valuation allowance, amount	0
Tax benefit attributable to non-U.S. government sponsored tax incentive programs	$ 58,300,000	$ 61,200,000	$ 59,100,000
Tax benefit per diluted share attributable to non-U.S. government sponsored tax incentive programs (in usd per share)	$ 0.50	$ 0.52	$ 0.51
Undistributed earnings of foreign subsidiaries	$ 120,400,000
Gross unrecognized tax benefits	3,900,000	$ 4,300,000	$ 25,500,000	$ 19,900,000
Accrued interest and penalties for unrecognized tax benefits	1,400,000	1,500,000
Benefits (expense) recognized for interest and penalties related to unrecognized tax benefits	0	$ 2,500,000	$ (700,000)
Reasonably possible amount of reduction of gross unrecognized tax benefit in the next twelve months	3,300,000
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	$ 4,700,000