Income Taxes - Differences Between Income Tax Provision (Benefit) and Income Taxes Computed using Applicable U.S. Statutory Federal Tax Rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Differences between the income tax provision (benefit) and income taxes computed using the applicable U.S. statutory federal tax rate
Income tax provision computed at federal statutory rate	$ 15,744	$ 1,983	$ 5,014
State income taxes, net of federal benefit	493	(630)	692
Foreign income taxed at different rates	132	550	920
Impact of investments in subsidiaries	296	(536)	(729)
Change in deferred tax asset valuation allowance	(1,526)	(2,264)	(75,918)
Net increase in uncertain tax positions	1,417	720	220
Global intangible low taxed income, net of foreign tax credits	611	1,389
Impact of tax rate change	262		15,287
Compensation	(3,022)	(1,103)	(701)
Tax credits	(2,845)	(2,741)	(1,633)
Merger costs	37	572	1,405
Other taxes	580	764	70
Non-deductible expenses	116	174	176
Transition tax		2,988	8,027
Deferred state rate change due to acquisition		(1,360)
Prior year true ups	(1,645)	(152)
Research and development expense deduction	(530)	(447)
Foreign derived intangible income	(153)
Other	(30)	(18)	(81)
Income tax provision (benefit)	$ 9,937	$ (111)	$ (47,251)