Income Taxes - Additional Information (Details) - USD ($)	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Income Tax Disclosure [Line Items]
Income taxes payable	$ 179,100,000	$ 75,300,000
Accrued income taxes	28,700,000	40,000,000
Prepaid income taxes	20,400,000	14,000,000
Income tax payments	121,700,000	68,600,000	$ 65,900,000
Foreign tax credits	5,996,000	2,028,000
Gross deferred amortization carryforward	18,000,000
Valuation allowance	8,529,000	21,755,000	21,695,000	$ 22,283,000
Interest Expense	77,019,000	119,653,000	129,417,000
Unrecognized tax benefit	157,724,000	65,035,000	50,742,000	$ 23,923,000
Penalty expense	0	0	0
Interest expense related to income tax accruals	13,600,000	3,100,000
Accrued tax penalties	0	0	0
Income tax provision upon recognition of unrecognized tax benefit	32,100,000
Unrecognized tax benefits, increase in valuation allowance upon recognition	6,000,000
Stock-based compensation	216,205,000	223,461,000	206,459,000
Tax benefit recognition related to stock based compensation	42,500,000	27,500,000	33,400,000
Provision (benefit) for income taxes	186,180,000	92,629,000	87,026,000
Income Tax Expense
Income Tax Disclosure [Line Items]
Interest Expense	10,000,000	3,300,000	500,000
Reversal of Associated Accrued Interest and Indirect Effects on GILTI and FDII
Income Tax Disclosure [Line Items]
Provision (benefit) for income taxes	(6,500,000)
Accrued Interest Stemming
Income Tax Disclosure [Line Items]
Provision (benefit) for income taxes	10,900,000	(4,400,000)
Domestic Country
Income Tax Disclosure [Line Items]
Valuation allowance	$ 3,400,000
Domestic Country | Minimum
Income Tax Disclosure [Line Items]
Credit carryforwards expiration	2026
Non-U.S. tax credit carryforwards expiration	2026
Domestic Country | Maximum
Income Tax Disclosure [Line Items]
Credit carryforwards expiration	2035
Non-U.S. tax credit carryforwards expiration	2033
Domestic Country | Expire in 2026 to 2033
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	$ 400,000
Domestic Country | Expiration beginning in 2026 and ending in 2035
Income Tax Disclosure [Line Items]
Credit carryforwards	2,200,000
State and Local Jurisdiction
Income Tax Disclosure [Line Items]
Valuation allowance	$ 3,400,000
State and Local Jurisdiction | Minimum
Income Tax Disclosure [Line Items]
Credit carryforwards expiration	2026
Non-U.S. tax credit carryforwards expiration	2027
State and Local Jurisdiction | Maximum
Income Tax Disclosure [Line Items]
Credit carryforwards expiration	2040
Non-U.S. tax credit carryforwards expiration	2042
State and Local Jurisdiction | Expiration Beginning in 2027
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	$ 4,900,000
State and Local Jurisdiction | Research Tax Credit Carryforward
Income Tax Disclosure [Line Items]
Credit carryforwards	16,800,000
Foreign Country
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	6,700,000
Credit carryforwards	6,000,000
Foreign tax credits	1,200,000
Valuation allowance	5,100,000
Provision (benefit) for income taxes	$ (10,800,000)	4,600,000
Tax credits		14,400,000
Foreign Country | Minimum
Income Tax Disclosure [Line Items]
Credit carryforwards expiration	2032
Non-U.S. tax credit carryforwards expiration	2031
Foreign Country | Maximum
Income Tax Disclosure [Line Items]
Credit carryforwards expiration	2035
Non-U.S. tax credit carryforwards expiration	2037
Windfall Tax Benefit
Income Tax Disclosure [Line Items]
Provision (benefit) for income taxes	$ (7,400,000)	(10,200,000)	(7,800,000)
Transfer Pricing Foreign Jurisdiction
Income Tax Disclosure [Line Items]
Uncertain tax			$ 21,800,000
Other Current Liabilities
Income Tax Disclosure [Line Items]
Accrued income taxes		6,200,000
Other Liabilities
Income Tax Disclosure [Line Items]
Accrued income taxes	150,400,000	$ 29,100,000
Other Liabilities | IRS Procedural Guidance Requiring Consent Domestic
Income Tax Disclosure [Line Items]
Unrecognized tax benefit	$ 109,200,000