Goodwill and Other Identifiable Intangible Assets, Net (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2023	Mar. 31, 2022	Mar. 31, 2023	Mar. 31, 2022	Sep. 30, 2022
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 435,773		$ 435,773		$ 435,651
Accumulated amortization	(146,332)		(146,332)		(133,587)
Net	289,441		289,441		302,064
Amortization expense			13,702	$ 16,098
Goodwill	341,862		341,862		340,477
Purchased and Core Technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	85,037		85,037		85,016
Accumulated amortization	(57,931)		(57,931)		(55,854)
Net	27,106		27,106		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	39,802		39,802		39,711
Accumulated amortization	(18,804)		(18,804)		(17,666)
Net	20,998		20,998		22,045
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	309,222		309,222		309,212
Accumulated amortization	(67,885)		(67,885)		(58,355)
Net	241,337		241,337		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	$ 6,200	$ 7,000	$ 12,700	$ 13,400