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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($)
$ in Thousands
3 Months Ended 9 Months Ended
Jun. 30, 2025
Jun. 30, 2024
Jun. 30, 2025
Jun. 30, 2024
Sep. 30, 2024
Finite-Lived Intangible Assets [Line Items]          
Gross carrying amount $ 436,814   $ 436,814   $ 436,311
Accumulated amortization (199,835)   (199,835)   (183,402)
Net 236,979   236,979   252,909
Goodwill 343,038   343,038   342,774
Purchased and Core Technology          
Finite-Lived Intangible Assets [Line Items]          
Gross carrying amount 85,018   85,018   85,041
Accumulated amortization (66,491)   (66,491)   (63,654)
Net 18,527   18,527   21,387
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 40,871   40,871   40,335
Accumulated amortization (24,252)   (24,252)   (22,047)
Net 16,619   16,619   18,288
Customer Relationships          
Finite-Lived Intangible Assets [Line Items]          
Gross carrying amount 309,213   309,213   309,223
Accumulated amortization (107,380)   (107,380)   (95,989)
Net 201,833   201,833   213,234
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 (1,000)   (1,000)   (1,000)
Net 0   0   $ 0
Cost of Sales and General and Administrative Expense          
Finite-Lived Intangible Assets [Line Items]          
Amortization expense $ 5,200 $ 6,100 $ 16,200 $ 18,400