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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($)
$ in Thousands
 3 Months Ended
Dec. 31, 2024
Dec. 31, 2023
Sep. 30, 2024
Finite-Lived Intangible Assets [Line Items]      
Gross carrying amount $ 436,432   $ 436,311
Accumulated amortization (189,221)   (183,402)
Net 247,211   252,909
Goodwill 341,234   342,774
Purchased and Core Technology      
Finite-Lived Intangible Assets [Line Items]      
Gross carrying amount 84,925   85,041
Accumulated amortization (64,492)   (63,654)
Net 20,433   21,387
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 40,624   40,335
Accumulated amortization (23,125)   (22,047)
Net 17,499   18,288
Customer Relationships      
Finite-Lived Intangible Assets [Line Items]      
Gross carrying amount 309,171   309,223
Accumulated amortization (99,892)   (95,989)
Net 209,279   213,234
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 $ 5,800 $ 6,200