Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2023	Dec. 31, 2022	Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 436,068		$ 435,897
Accumulated amortization	(165,147)		(158,813)
Net	270,921		277,084
Amortization expense	6,591	$ 6,957
Goodwill	342,424		341,593
Purchased and Core Technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	85,080		85,032
Accumulated amortization	(60,833)		(59,833)
Net	24,247		25,199
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	40,035		39,957
Accumulated amortization	(20,421)		(19,888)
Net	19,614		20,069
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	309,241		309,196
Accumulated amortization	(82,181)		(77,380)
Net	227,060		231,816
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	$ 6,200	$ 6,500