Fair Value of Financial Instruments - Contingent Consideration (Details) $ in Thousands, item in Millions	12 Months Ended
	Sep. 30, 2020 USD ($) item	Sep. 30, 2019 USD ($)	Jan. 03, 2020 USD ($)	Sep. 30, 2018 USD ($)
Assets and liabilities measured at fair value on a recurring basis
Assets	$ 2,324,221	$ 1,847,170		$ 1,304,900
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
Investment	5,600	5,300
Franklin Blackhorse, L.P | Other income (expense)
Assets and liabilities measured at fair value on a recurring basis
Net loss from equity method investment	1,100	300
Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period	10,874	9,114
Initial measurement recognized at acquisition	1,600	4,900
Cash paid to seller		(2,135)
Total remeasurement (gain) loss recognized in earnings	(1,856)	(1,005)
Balance at the ending period	10,618	10,874
TeraLogics | Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period		1,750
Cash paid to seller		(1,750)
H4 Global | Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period	1,073	665
Cash paid to seller		(385)
Total remeasurement (gain) loss recognized in earnings	75	793
Balance at the ending period	1,148	1,073
H4 Global | Maximum
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration for certain goals	2,800
Deltenna | Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period	1,787	1,081
Total remeasurement (gain) loss recognized in earnings	1,217	706
Balance at the ending period	3,004	$ 1,787
Deltenna | Maximum
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration for certain goals	$ 7,000
Deltenna | Volatility for underlying revenue metrics
Assets and liabilities measured at fair value on a recurring basis
Measurement inputs for contingent consideration	52	36
Deltenna | Discount Rate
Assets and liabilities measured at fair value on a recurring basis
Measurement inputs for contingent consideration	10.5	11.0
Shield Aviation
Assets and liabilities measured at fair value on a recurring basis
Determination of fair value of contingent consideration | item	1
Revenue risk adjustment used in determination of fair value of contingent consideration	16.00%	13.10%
Shield Aviation | Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period	$ 3,814	$ 5,618
Total remeasurement (gain) loss recognized in earnings	1,752	(1,804)
Balance at the ending period	5,566	$ 3,814
Shield Aviation | Maximum
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration	$ 10,000
Shield Aviation | Volatility for underlying revenue metrics
Assets and liabilities measured at fair value on a recurring basis
Volatility for underlying earnings metrics used in determination of fair value of contingent consideration	31.00%	18.00%
Shield Aviation | Discount Rate
Assets and liabilities measured at fair value on a recurring basis
Measurement inputs for contingent consideration	5.7	3.6
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 | Level 3
Change in fair value of our Level 3 contingent consideration
Balance at the Beginning period	4,200
Initial measurement recognized at acquisition		$ 4,900
Total remeasurement (gain) loss recognized in earnings	(4,200)	(700)
Balance at the ending period		$ 4,200
Nuvotronics | Maximum
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration	$ 8,000
Delerrok Inc.
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration			$ 1,600
Period for contingent consideration contracts	12 months
Delerrok Inc. | Level 3
Change in fair value of our Level 3 contingent consideration
Initial measurement recognized at acquisition	$ 1,600
Total remeasurement (gain) loss recognized in earnings	(700)
Balance at the ending period	900
Delerrok Inc. | Maximum
Assets and liabilities measured at fair value on a recurring basis
Contingent consideration for certain goals	$ 2,000
Delerrok Inc. | Volatility for underlying revenue metrics
Assets and liabilities measured at fair value on a recurring basis
Measurement inputs for contingent consideration	14
Delerrok Inc. | Discount Rate
Assets and liabilities measured at fair value on a recurring basis
Measurement inputs for contingent consideration	3.4