Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Jun. 30, 2023	Jun. 30, 2022	Jun. 30, 2023	Jun. 30, 2022	Sep. 30, 2022
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 435,936		$ 435,936		$ 435,651
Accumulated amortization	(152,648)		(152,648)		(133,587)
Net	283,288		283,288		302,064
Amortization expense			20,449	$ 23,638
Goodwill	342,292		342,292		340,477
Purchased and Core Technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	85,080		85,080		85,016
Accumulated amortization	(58,927)		(58,927)		(55,854)
Net	26,153		26,153		29,162
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	39,903		39,903		39,711
Accumulated amortization	(19,344)		(19,344)		(17,666)
Net	20,559		20,559		22,045
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	309,241		309,241		309,212
Accumulated amortization	(72,665)		(72,665)		(58,355)
Net	236,576		236,576		250,857
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	$ 6,300	$ 7,000	$ 19,000	$ 20,400