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Income Taxes - Additional Information (Details) - USD ($) | 12 Months Ended |
--- | --- | ---
Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020
Income Tax Disclosure [Line Items] |  |  |  |
Income taxes payable | $ 30,400,000 | $ 17,300,000 |  |
Accrued income taxes | 14,900,000 | 5,100,000 |  |
Prepaid income taxes | 22,700,000 | 25,800,000 |  |
Income tax payments | 65,900,000 | 55,000,000 | $ 56,000,000 |
Foreign tax credits | 3,750,000 | 14,527,000 |  |
Gross deferred amortization carryforward | 85,300,000 |  |  |
Valuation allowance | 21,695,000 | 22,283,000 | 52,085,000 | $ 205,423,000
Interest Expense | 129,417,000 | 54,268,000 | 50,478,000 |
Penalty expense | 0 | 0 | 2,000,000 |
Interest expense related to income tax accruals | 1,400,000 | 900,000 |  |
Accrued tax penalties | 0 | 0 | 0 |
Income tax provision upon recognition of unrecognized tax benefit | 50,700,000 |  |  |
Unrecognized tax benefits, increase in valuation allowance upon recognition | 5,700,000 |  |  |
Potential decrease in unrecognized tax benefits | 26,000,000 |  |  |
Charge related to effects of Non US Jurisdiction Tax Matter |  |  | 37,300,000 |
US Income taxes on repatriated foreign earnings |  |  | 2,900,000 |
Stock-based compensation | 206,459,000 | 174,863,000 | 177,289,000 |
Tax benefit recognition related to stock based compensation | 33,400,000 | 27,100,000 | 39,900,000 |
Provision (benefit) for income taxes | 87,026,000 | 84,017,000 | (85,168,000) |
Income Tax Expense |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Interest Expense | 500,000 | 200,000 | 2,200,000 |
Domestic Country |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | 6,400,000 |  |  |
Valuation allowance | $ 17,400,000 |  |  |
Domestic Country | Minimum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards expiration | 2025 |  |  |
Domestic Country | Maximum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards expiration | 2043 |  |  |
Domestic Country | Expire in 2023 to 2036 |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | $ 1,200,000 |  |  |
Credit carryforwards | 46,700,000 |  |  |
Domestic Country | Not Expire |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | 5,200,000 |  |  |
State - Massachusetts |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Valuation allowance | $ 17,400,000 |  |  |
State - Massachusetts | Minimum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards expiration | 2024 |  |  |
State - Massachusetts | Maximum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards expiration | 2038 |  |  |
State - Massachusetts | Research Tax Credit Carryforward |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards | $ 27,300,000 |  |  |
Foreign Country |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | 6,800,000 |  |  |
Credit carryforwards | 3,700,000 |  |  |
Foreign tax credits | 2,300,000 |  |  |
Valuation allowance | $ 4,300,000 |  |  |
Foreign Country | Minimum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards expiration | 2030 |  |  |
Non-U.S. tax credit carryforwards expiration | 2030 |  |  |
Foreign Country | Maximum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards expiration | 2033 |  |  |
Non-U.S. tax credit carryforwards expiration | 2041 |  |  |
REPUBLIC OF KOREA |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Charge related to effects of Non US Jurisdiction Tax Matter |  |  | 34,400,000 |
Payment related to effects of Non US jurisdiction tax matter |  |  | 20,000,000 |
Windfall Tax Benefit |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Provision (benefit) for income taxes | $ (7,800,000) | (5,200,000) | $ (9,900,000) |
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 | 4,800,000 | 5,600,000 |  |
Other Liabilities [Member] |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Accrued income taxes | $ 10,700,000 | $ 6,600,000 |  |

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