Stockholders' Equity - Accumulated Other Comprehensive Income (Loss) (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2023	Dec. 31, 2022
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	$ 2,534,500	$ 3,363,386
Ending Balance	2,443,664	2,871,389
Accumulated Other Comprehensive Income (Loss)
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(62,426)	(83,916)
Other comprehensive income (loss) before reclassifications	35,615	21,842
Amounts reclassified from accumulated other comprehensive income (loss)	27
Ending Balance	(26,784)	(62,074)
Currency Translation Adjustments
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(88,448)	(165,694)
Other comprehensive income (loss) before reclassifications	46,494	77,414
Ending Balance	(41,954)	(88,280)
Unrealized Gains (Losses) on Available-for-Sale Securities, Net of Tax
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(5,135)	(10,909)
Other comprehensive income (loss) before reclassifications	2,524	1,555
Ending Balance	(2,611)	(9,354)
Unrealized Gain on Derivative Asset, Net of Tax
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	31,487	93,020
Other comprehensive income (loss) before reclassifications	(13,368)	(57,127)
Ending Balance	18,119	35,893
Pension Liability Adjustments
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(330)	(333)
Other comprehensive income (loss) before reclassifications	(35)
Amounts reclassified from accumulated other comprehensive income (loss)	27
Ending Balance	$ (338)	$ (333)