Income Taxes - Reconciliation Between Federal Statutory Income Tax Rate and Effective Tax Rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Income Tax Disclosure [Abstract]
Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent	21.00%
Effective Income Tax Rate Reconciliation at Federal Statutory Income Tax Rate, Amount	$ 98,975	$ 99,360	$ 53,970
Effective Income Tax Rate Reconciliation, State and Local Income Taxes, Amount	8,359	7,815	4,619
Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Amount	3,058	1,490	493
Effective Income Tax Rate Reconciliation, Tax Credit, Research, Amount	(5,932)	(6,795)	(5,868)
Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Amount	(11,768)	3,839	5,332
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-based Payment Arrangement, Amount	702	(15,573)	(45,086)
GILTI, FDII and BEAT	(2,491)	(4,958)	7,136
Effective Income Tax Rate Reconciliation, Other Adjustments, Amount	6,865	(4,120)	(7)
Total provision	$ 97,768	$ 81,058	$ 20,589