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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands | 3 Months Ended |
--- | --- | ---
Dec. 31, 2023 | Dec. 31, 2022 | Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items] |  |  |
Gross carrying amount | $ 436,068 |  | $ 435,897
Accumulated amortization | (165,147) |  | (158,813)
Net | 270,921 |  | 277,084
Amortization expense | 6,591 | $ 6,957 |
Goodwill | 342,424 |  | 341,593
Purchased and Core Technology |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Gross carrying amount | 85,080 |  | 85,032
Accumulated amortization | (60,833) |  | (59,833)
Net | 24,247 |  | 25,199
License Agreements |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Gross carrying amount | 112 |  | 112
Accumulated amortization | (112) |  | (112)
Net | 0 |  | 0
Patents and Trademarks |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Gross carrying amount | 40,035 |  | 39,957
Accumulated amortization | (20,421) |  | (19,888)
Net | 19,614 |  | 20,069
Customer Relationships |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Gross carrying amount | 309,241 |  | 309,196
Accumulated amortization | (82,181) |  | (77,380)
Net | 227,060 |  | 231,816
Non-compete Agreements |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Gross carrying amount | 600 |  | 600
Accumulated amortization | (600) |  | (600)
Net | 0 |  | 0
Order backlog |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Gross carrying amount | 1,000 |  | 1,000
Accumulated amortization | (1,000) |  | (1,000)
Net | 0 |  | $ 0
Cost of Sales and General and Administrative Expense |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Amortization expense | $ 6,200 | $ 6,500 |

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