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Income Taxes - Additional Information (Details) - USD ($) $ in Thousands | 12 Months Ended |
--- | --- | ---
Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020 | Sep. 30, 2019
Income Tax Disclosure [Line Items] |  |  |  |
Income taxes payable | $ 17,300 | $ 15,700 |  |
Accrued income taxes | 5,100 | 5,000 |  |
Prepaid income taxes | 25,800 | 15,400 |  |
Income tax payments | 55,000 | 56,000 | $ 52,600 |
Non-cash federal |  | 109,400 |  |
State tax benefits |  | 24,800 |  |
Foreign tax credits | 14,527 | 36,287 |  |
Gross deferred amortization carryforward | 118,500 |  |  |
Valuation allowance | 22,283 | 52,085 | 205,423 | $ 177,663
Interest Expense | 54,268 | 50,478 | 76,428 |
Penalty expense | 0 | 2,000 | 0 |
Interest expense related to income tax accruals | 900 | 700 |  |
Accrued tax penalties | 0 | 0 | 0 |
Income tax provision upon recognition of unrecognized tax benefit | 23,900 |  |  |
Unrecognized tax benefits, increase in valuation allowance upon recognition | 5,200 |  |  |
Potential decrease in unrecognized tax benefits | 5,000 |  |  |
Charge related to effects of Non US Jurisdiction Tax Matter |  | 37,300 |  |
US Income taxes on repatriated foreign earnings |  | 2,900 |  |
Stock-based compensation | 174,863 | 177,289 | 115,149 |
Tax benefit recognition related to stock based compensation | 27,100 | 39,900 | 13,400 |
Provision (benefit) for income taxes | 84,017 | (85,168) | 4,011 |
Income Tax Expense |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Interest Expense | 200 | 2,200 | 300 |
Domestic Country |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | 22,500 |  |  |
Valuation allowance | 17,800 |  |  |
Domestic Country | Expire in 2023 to 2036 |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | 1,600 |  |  |
Credit carryforwards | 60,900 |  |  |
Domestic Country | Not Expire |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | 20,900 |  |  |
State - Massachusetts |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Valuation allowance |  | 17,800 |  |
State - Massachusetts | Research Tax Credit Carryforward |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Credit carryforwards | 26,100 |  |  |
Foreign Country |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Net operating loss carryforwards | 7,200 |  |  |
Credit carryforwards | $ 14,500 |  |  |
Credit carryforwards expiration | 2027 |  |  |
Foreign tax credits | $ 4,000 |  |  |
Valuation allowance | $ 4,500 |  |  |
Foreign Country | Minimum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Non-U.S. tax credit carryforwards expiration | 2030 |  |  |
Foreign Country | Maximum |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
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 |  |
Payment related to effects of Non US jurisdiction tax matter |  | 20,000 |  |
Windfall Tax Benefit |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Provision (benefit) for income taxes | $ 5,200 | 9,900 | $ 1,300 |
Other Current Liabilities |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Accrued income taxes | 5,600 | 800 |  |
Other Liabilities [Member] |  |  |  |
Income Tax Disclosure [Line Items] |  |  |  |
Accrued income taxes | $ 6,600 | $ 9,900 |  |

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