Fair Value of Financial Instruments - Contingent Consideration (Details) $ in Thousands, item in Millions		6 Months Ended	12 Months Ended
	Jan. 31, 2021 USD ($)	Mar. 31, 2021 USD ($) item	Sep. 30, 2020 USD ($)	Sep. 30, 2021 USD ($)	Jan. 03, 2020 USD ($)	Sep. 30, 2019 USD ($)	Sep. 30, 2018 USD ($)
Assets and liabilities measured at fair value on a recurring basis
Assets		$ 2,401,458	$ 2,324,221
Franklin Blackhorse, L.P
Assets and liabilities measured at fair value on a recurring basis
Investment			1,200			$ 5,000
Franklin Blackhorse, L.P | Other Assets
Assets and liabilities measured at fair value on a recurring basis
Assets		7,300	5,600
Franklin Blackhorse, L.P | Forecast
Assets and liabilities measured at fair value on a recurring basis
Investment				$ 1,400
Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period		10,618
Cash paid to seller		(1,286)
Total remeasurement (gain) loss recognized in earnings		684
Balance at the ending period		10,016	10,618
H4 Global
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration for certain goals	$ 1,300
Contingent consideration		0
H4 Global | Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period		1,148
Cash paid to seller		(1,286)
Total remeasurement (gain) loss recognized in earnings		138
Balance at the ending period			1,148
Deltenna | Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period		3,004
Total remeasurement (gain) loss recognized in earnings		201
Balance at the ending period		3,205	$ 3,004
Deltenna | Maximum
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration for certain goals		$ 7,400
Deltenna | Volatility for underlying revenue metrics
Assets and liabilities measured at fair value on a recurring basis
Measurement inputs for contingent consideration		52	52
Deltenna | Discount Rate
Assets and liabilities measured at fair value on a recurring basis
Measurement inputs for contingent consideration		10.5	10.5
Shield Aviation
Assets and liabilities measured at fair value on a recurring basis
Determination of fair value of contingent consideration | item		1
Volatility for underlying earnings metrics used in determination of fair value of contingent consideration		26.00%	31.00%
Revenue risk adjustment used in determination of fair value of contingent consideration		13.00%	16.00%
Shield Aviation | Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period		$ 5,566
Total remeasurement (gain) loss recognized in earnings		1,245
Balance at the ending period		6,811	$ 5,566
Shield Aviation | Maximum
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration for certain goals		$ 10,000
Shield Aviation | Discount Rate
Assets and liabilities measured at fair value on a recurring basis
Measurement inputs for contingent consideration		5.3	5.7
Nuvotronics
Assets and liabilities measured at fair value on a recurring basis
Determination of fair value of contingent consideration | item		1
Period for contingent consideration contracts		12 months
Contingent consideration, fair value		$ 0
Nuvotronics | Maximum
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration for certain goals		8,000
Delerrok Inc.
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration					$ 1,600
Investment						$ 8,300	$ 8,300
Contingent consideration, fair value		0
Delerrok Inc. | Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period		900
Total remeasurement (gain) loss recognized in earnings		$ (900)
Balance at the ending period			$ 900