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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($)
$ in Thousands
 3 Months Ended 9 Months Ended
Jun. 30, 2024
Jun. 30, 2023
Jun. 30, 2024
Jun. 30, 2023
Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items]          
Gross carrying amount $ 436,123   $ 436,123   $ 435,897
Accumulated amortization (177,255)   (177,255)   (158,813)
Net 258,868   258,868   277,084
Goodwill 341,916   341,916   341,593
Purchased and Core Technology          
Finite-Lived Intangible Assets [Line Items]          
Gross carrying amount 85,018   85,018   85,032
Accumulated amortization (62,678)   (62,678)   (59,833)
Net 22,340   22,340   25,199
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 40,180   40,180   39,957
Accumulated amortization (21,495)   (21,495)   (19,888)
Net 18,685   18,685   20,069
Customer Relationships          
Finite-Lived Intangible Assets [Line Items]          
Gross carrying amount 309,213   309,213   309,196
Accumulated amortization (91,370)   (91,370)   (77,380)
Net 217,843   217,843   231,816
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 $ 6,100 $ 6,300 $ 18,400 $ 19,000