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Income Taxes - Additional Information (Details) - USD ($) | 12 Months Ended |
--- | --- | ---
Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
Income Tax Disclosure [Line Items] |  |  |  |
Income taxes payable | $ 75,300,000 | $ 30,400,000 |  |
Accrued income taxes | 40,000,000 | 14,900,000 |  |
Prepaid income taxes | 14,000,000 | 22,700,000 |  |
Income tax payments | 68,600,000 | 65,900,000 | $ 55,000,000 |
Foreign tax credits | 2,028,000 | 3,750,000 |  |
Gross deferred amortization carryforward | 66,100,000 |  |  |
Valuation allowance | 21,755,000 | 21,695,000 | 22,283,000 | $ 52,085,000
Interest Expense | 119,653,000 | 129,417,000 | 54,268,000 |
Penalty expense | 0 | 0 | 0 |
Interest expense related to income tax accruals | 3,100,000 | 1,400,000 |  |
Accrued tax penalties | 0 | 0 | 0 |
Income tax provision upon recognition of unrecognized tax benefit | 65,000,000 |  |  |
Unrecognized tax benefits, increase in valuation allowance upon recognition | 6,200,000 |  |  |
Potential decrease in unrecognized tax benefits | 27,000,000 |  |  |
Stock-based compensation | 223,461,000 | 206,459,000 | 174,863,000 |
Tax benefit recognition related to stock based compensation | 27,500,000 | 33,400,000 | 27,100,000 |
Provision (benefit) for income taxes | 92,629,000 | 87,026,000 | 84,017,000 |
Income Tax Expense |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Interest Expense | 3,300,000 | 500,000 | 200,000 |
IRS Procedural Guidance Requiring Consent Domestic |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Provision (benefit) for income taxes | 4,400,000 |  |  |
Domestic Country |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Valuation allowance | $ 17,400,000 |  |  |
Domestic Country | Minimum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards expiration | 2026 |  |  |
Domestic Country | Maximum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards expiration | 2044 |  |  |
Domestic Country | Expire in 2025 to 2034 |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | $ 800,000 |  |  |
Domestic Country | Expiration Beginning in 2026 and Ending in 2044 |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards | 4,600,000 |  |  |
State - Massachusetts |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Valuation allowance | $ 17,400,000 |  |  |
State - Massachusetts | Minimum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards expiration | 2025 |  |  |
State - Massachusetts | Maximum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards expiration | 2039 |  |  |
State - Massachusetts | Expiration Beginning in 2027 |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | $ 6,900,000 |  |  |
State - Massachusetts | Research Tax Credit Carryforward |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards | 29,200,000 |  |  |
Foreign Country |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | 6,900,000 |  |  |
Credit carryforwards | 2,000,000 |  |  |
Foreign tax credits | 2,200,000 |  |  |
Valuation allowance | 4,400,000 |  |  |
Provision (benefit) for income taxes | 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 | 2034 |  |  |
Non-U.S. tax credit carryforwards expiration | 2042 |  |  |
Windfall Tax Benefit |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Provision (benefit) for income taxes | $ (10,200,000) | (7,800,000) | $ (5,200,000) |
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 | 4,800,000 |  |
Other Liabilities [Member] |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Accrued income taxes | $ 29,100,000 | $ 10,700,000 |  |

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