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Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020	Sep. 30, 2020
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 231,617		$ 231,617		$ 225,059
Accumulated amortization	(116,635)		(116,635)		(103,811)
Net	114,982		114,982		121,248
Amortization expense			11,989	$ 10,687
Goodwill	221,331		221,331		210,135
Purchased and Core Technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	77,624		77,624		76,011
Accumulated amortization	(59,264)		(59,264)		(55,482)
Net	18,360		18,360		20,529
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	23,591		23,591		22,836
Accumulated amortization	(14,806)		(14,806)		(13,535)
Net	8,785		8,785		9,301
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	129,690		129,690		125,500
Accumulated amortization	(41,913)		(41,913)		(34,232)
Net	87,777		87,777		91,268
Non-compete Agreements
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	600		600		600
Accumulated amortization	(540)		(540)		(450)
Net	60		60		$ 150
Cost of Sales and General and Administrative Expense
Finite-Lived Intangible Assets [Line Items]
Amortization expense	$ 4,100	$ 4,100	$ 12,000	$ 10,700

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