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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($)
$ in Thousands
 3 Months Ended 6 Months Ended
Mar. 31, 2025
Mar. 31, 2024
Mar. 31, 2025
Mar. 31, 2024
Sep. 30, 2024
Finite-Lived Intangible Assets [Line Items]          
Gross carrying amount $ 436,527   $ 436,527   $ 436,311
Accumulated amortization (194,461)   (194,461)   (183,402)
Net 242,066   242,066   252,909
Goodwill 341,669   341,669   342,774
Purchased and Core Technology          
Finite-Lived Intangible Assets [Line Items]          
Gross carrying amount 84,928   84,928   85,041
Accumulated amortization (65,448)   (65,448)   (63,654)
Net 19,480   19,480   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 40,714   40,714   40,335
Accumulated amortization (23,684)   (23,684)   (22,047)
Net 17,030   17,030   18,288
Customer Relationships          
Finite-Lived Intangible Assets [Line Items]          
Gross carrying amount 309,173   309,173   309,223
Accumulated amortization (103,617)   (103,617)   (95,989)
Net 205,556   205,556   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 $ 11,000 $ 12,300