Stockholders' Equity - Accumulated Other Comprehensive Income (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	$ 3,363,386	$ 1,325,334	$ 1,213,614
Ending Balance	2,534,500	3,363,386	1,325,334
Accumulated Other Comprehensive Income (Loss)
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(83,916)	19,351	21,919
Other comprehensive income (loss) before reclassifications	21,383	(86,742)	(2,589)
Amounts reclassified from accumulated other comprehensive income (loss)	107	(16,525)	21
Ending Balance	(62,426)	(83,916)	19,351
Currency Translation Adjustments
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(165,694)	20,139	23,061
Other comprehensive income (loss) before reclassifications	77,246	(169,266)	(2,922)
Amounts reclassified from accumulated other comprehensive income (loss)		(16,567)
Ending Balance	(88,448)	(165,694)	20,139
Unrealized Gains (Losses) on Available-for-Sale Securities
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(10,909)	(1)	(1)
Other comprehensive income (loss) before reclassifications	5,774	(10,908)
Ending Balance	(5,135)	(10,909)	(1)
Unrealized Gain on Derivative Asset Net of Tax
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	93,020
Other comprehensive income (loss) before reclassifications	(61,533)	93,020
Ending Balance	31,487	93,020
Pension Liability Adjustments
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(333)	(787)	(1,141)
Other comprehensive income (loss) before reclassifications	(104)	412	333
Amounts reclassified from accumulated other comprehensive income (loss)	107	42	21
Ending Balance	$ (330)	$ (333)	$ (787)