Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Sep. 30, 2021
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 435,711		$ 224,643
Accumulated amortization	(112,917)		(106,614)
Net	322,794		118,029
Amortization expense	6,309	$ 3,961
Goodwill	342,498		225,522
Purchased and Core Technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	85,162		69,162
Accumulated amortization	(52,090)		(50,701)
Net	33,072		18,461
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	39,559		23,491
Accumulated amortization	(15,576)		(14,978)
Net	23,983		8,513
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	309,278		130,278
Accumulated amortization	(44,039)		(39,973)
Net	265,239		90,305
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	(500)		(250)
Net	500		$ 750
Cost of Sales and General and Administrative Expense
Finite-Lived Intangible Assets [Line Items]
Amortization expense	$ 6,300	$ 4,000