Stockholders' Equity - Accumulated Other Comprehensive Income (Loss) (Details) - USD ($) $ in Thousands	6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	$ 2,534,500	$ 3,363,386
Ending Balance	2,222,871	2,895,227
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	20,652	45,046
Amounts reclassified from accumulated other comprehensive income (loss)	46
Ending Balance	(41,728)	(38,870)
Currency Translation Adjustments
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(88,448)	(165,694)
Other comprehensive income (loss) before reclassifications	25,725	111,264
Ending Balance	(62,723)	(54,430)
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	3,276	4,042
Ending Balance	(1,859)	(6,867)
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	(8,288)	(70,260)
Ending Balance	23,199	22,760
Pension Liability Adjustments
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(330)	(333)
Other comprehensive income (loss) before reclassifications	(61)
Amounts reclassified from accumulated other comprehensive income (loss)	46
Ending Balance	$ (345)	$ (333)