Goodwill and Intangible Assets - Components of Identifiable Intangible Assets (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Sep. 30, 2020
Finite-Lived Intangible Assets [Line Items]
Cost	$ 408,011	$ 394,906
Accumulated Amortization	188,145	176,581
Net Book Value	219,866	218,325
Patents
Finite-Lived Intangible Assets [Line Items]
Cost	5,302	5,302
Accumulated Amortization	4,914	4,865
Net Book Value	388	437
Completed Technology
Finite-Lived Intangible Assets [Line Items]
Cost	93,644	92,477
Accumulated Amortization	52,847	49,875
Net Book Value	40,797	42,602
Trademarks and Trade Names
Finite-Lived Intangible Assets [Line Items]
Cost	26,253	25,769
Accumulated Amortization	10,222	9,322
Net Book Value	16,031	16,447
Noncompete Agreements
Finite-Lived Intangible Assets [Line Items]
Cost	703
Accumulated Amortization	61
Net Book Value	642
Customer Relationships
Finite-Lived Intangible Assets [Line Items]
Cost	281,852	271,113
Accumulated Amortization	119,847	112,277
Net Book Value	162,005	158,836
Other Intangible Assets
Finite-Lived Intangible Assets [Line Items]
Cost	257	245
Accumulated Amortization	254	242
Net Book Value	$ 3	$ 3