Goodwill and Intangible Assets - Components of Identifiable Intangible Assets (Details) - USD ($) $ in Thousands	Dec. 31, 2023	Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items]
Cost	$ 527,854	$ 515,636
Accumulated Amortization	237,625	221,335
Net Book Value	290,229	294,301
Patents
Finite-Lived Intangible Assets [Line Items]
Cost	1,226	1,226
Accumulated Amortization	1,180	1,175
Net Book Value	46	51
Completed Technology
Finite-Lived Intangible Assets [Line Items]
Cost	222,259	215,430
Accumulated Amortization	62,712	56,021
Net Book Value	159,547	159,409
Trademarks and Trade Names
Finite-Lived Intangible Assets [Line Items]
Cost	6,902	6,630
Accumulated Amortization	1,900	1,445
Net Book Value	5,002	5,185
Non-competition agreements
Finite-Lived Intangible Assets [Line Items]
Cost	681	681
Accumulated Amortization	588	568
Net Book Value	93	113
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Cost	295,879	290,800
Accumulated Amortization	170,338	161,257
Net Book Value	125,541	129,543
Other Intangible Assets
Finite-Lived Intangible Assets [Line Items]
Cost	907	869
Accumulated Amortization	$ 907	$ 869