Summary of Significant Accounting Policies - Derivative Financial Instruments (Details) - USD ($)	1 Months Ended	3 Months Ended	12 Months Ended
	Sep. 30, 2019	Dec. 31, 2020	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020	Sep. 25, 2019	Jul. 09, 2010
Derivative [Line Items]
Accumulated other comprehensive income (loss) on derivative instruments, tax			$ (700,000)	$ (700,000)
Other			8,400,000	300,000	$ 4,000,000.0
Accumulated Other Comprehensive Income (Loss), Cumulative Changes in Net Gain (Loss) from Cash Flow Hedges, Effect Net of Tax			(9,100,000)	(10,200,000)
Carrying Value
Derivative [Line Items]
Derivative Asset			3,000,000.0	1,900,000
Derivative Liability			8,000,000.0	2,500,000
Cash Flow Hedging | Foreign Exchange Forward [Member]
Derivative [Line Items]
Derivative Instruments and Hedges, Assets			173,100,000	186,400,000
Cash Flow Hedging | Interest Rate Swap [Member]
Derivative [Line Items]
Derivative Instruments and Hedges, Liabilities			20,200,000
Accumulated Other Comprehensive Income (Loss), Cumulative Changes in Net Gain (Loss) from Cash Flow Hedges, Effect Net of Tax			$ 13,800,000
Maximum
Derivative [Line Items]
Length of Time Hedged in Currency Exchange Rates			24 months
Senior unsecured notes
Derivative [Line Items]
Debt issued						$ 375,000,000.0
Term of debt instrument	7 years
$150.0 senior unsecured notes
Derivative [Line Items]
Debt issued							$ 150,000,000.0
Term of debt instrument		10 years
Reclassification out of Accumulated Other Comprehensive Income
Derivative [Line Items]
Other			$ 5,900,000	(2,000,000.0)	9,100,000
Interest expense, interest rate swap amortization over next twelve months			2,000,000.0
Reclassification out of Accumulated Other Comprehensive Income | Interest Rate Swap [Member]
Derivative [Line Items]
Other			6,400,000
Net Unrealized Gain (Loss) on Derivative Instruments | Reclassification out of Accumulated Other Comprehensive Income
Derivative [Line Items]
Other			$ 1,900,000	$ 1,900,000	$ (2,000,000.0)