Goodwill and Intangible Assets - Components of Identifiable Intangible Assets (Details) - USD ($) $ in Thousands	Jun. 30, 2021	Sep. 30, 2020
Finite-Lived Intangible Assets [Line Items]
Cost	$ 464,034	$ 394,906
Accumulated Amortization	209,098	176,581
Net Book Value	254,937	218,325
Patents
Finite-Lived Intangible Assets [Line Items]
Cost	5,302	5,302
Accumulated Amortization	5,013	4,865
Net Book Value	289	437
Completed Technology
Finite-Lived Intangible Assets [Line Items]
Cost	144,440	92,477
Accumulated Amortization	58,118	49,875
Net Book Value	86,323	42,602
Trademarks and Trade Names
Finite-Lived Intangible Assets [Line Items]
Cost	27,625	25,769
Accumulated Amortization	12,102	9,322
Net Book Value	15,523	16,447
Noncompete Agreements
Finite-Lived Intangible Assets [Line Items]
Cost	731
Accumulated Amortization	129
Net Book Value	601
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Cost	285,685	271,113
Accumulated Amortization	133,488	112,277
Net Book Value	152,197	158,836
Other Intangible Assets
Finite-Lived Intangible Assets [Line Items]
Cost	251	245
Accumulated Amortization	248	242
Net Book Value	$ 3	$ 3