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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands | 3 Months Ended | 6 Months Ended |
--- | --- | --- | ---
Mar. 31, 2022 | Mar. 31, 2021 | Mar. 31, 2022 | Mar. 31, 2021 | Sep. 30, 2021
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | $ 435,806 |  | $ 435,806 |  | $ 224,643
Accumulated amortization | (120,009) |  | (120,009) |  | (106,614)
Net | 315,797 |  | 315,797 |  | 118,029
Amortization expense |  |  | 13,354 | $ 7,888 |
Goodwill | 341,645 |  | 341,645 |  | 225,522
Purchased and Core Technology |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 85,194 |  | 85,194 |  | 69,162
Accumulated amortization | (53,425) |  | (53,425) |  | (50,701)
Net | 31,769 |  | 31,769 |  | 18,461
License Agreements |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 112 |  | 112 |  | 112
Accumulated amortization | (112) |  | (112) |  | (112)
Net | 0 |  | 0 |  | 0
Patents and Trademarks |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 39,608 |  | 39,608 |  | 23,491
Accumulated amortization | (16,276) |  | (16,276) |  | (14,978)
Net | 23,332 |  | 23,332 |  | 8,513
Customer Relationships |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 309,292 |  | 309,292 |  | 130,278
Accumulated amortization | (48,846) |  | (48,846) |  | (39,973)
Net | 260,446 |  | 260,446 |  | 90,305
Non-compete Agreements |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 600 |  | 600 |  | 600
Accumulated amortization | (600) |  | (600) |  | (600)
Net | 0 |  | 0 |  | 0
Order backlog |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Gross carrying amount | 1,000 |  | 1,000 |  | 1,000
Accumulated amortization | (750) |  | (750) |  | (250)
Net | 250 |  | 250 |  | $ 750
Cost of Sales and General and Administrative Expense |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Amortization expense | $ 7,000 | $ 3,900 | $ 13,400 | $ 7,900 |

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