Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2022	Mar. 31, 2021	Sep. 30, 2021
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 435,806		$ 435,806		$ 224,643
Accumulated amortization	(120,009)		(120,009)		(106,614)
Net	315,797		315,797		118,029
Amortization expense			13,354	$ 7,888
Goodwill	341,645		341,645		225,522
Purchased and Core Technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	85,194		85,194		69,162
Accumulated amortization	(53,425)		(53,425)		(50,701)
Net	31,769		31,769		18,461
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	39,608		39,608		23,491
Accumulated amortization	(16,276)		(16,276)		(14,978)
Net	23,332		23,332		8,513
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	309,292		309,292		130,278
Accumulated amortization	(48,846)		(48,846)		(39,973)
Net	260,446		260,446		90,305
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	(750)		(750)		(250)
Net	250		250		$ 750
Cost of Sales and General and Administrative Expense
Finite-Lived Intangible Assets [Line Items]
Amortization expense	$ 7,000	$ 3,900	$ 13,400	$ 7,900