Income Taxes - Schedule of Difference Between Federal Statutory Rate and the Effective Tax Rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2023
Rate Reconciliation, Amount
Tax at federal statutory rate	$ 192,300	$ 150,800	$ 44,800
State income tax, net of federal benefit	16,100	(8,500)	(7,100)
Change in uncertain tax positions	46,700	18,600	9,400
Foreign residual income	41,900	43,800	59,400
Nondeductible costs	16,600	20,600	10,700
Tax rate changes	2,300	1,200	(3,200)
Audit settlement	1,400	500	1,900
Income tax credits and incentives	(59,500)	(63,500)	(68,200)
Legal entity restructuring	20,100	0	0
Exclusion of tax on non-controlling interests	(15,600)	(12,500)	(9,400)
Valuation allowance	(11,800)	(12,600)	16,600
Tax exempt income	(2,100)	(2,500)	(3,300)
Foreign tax rate differential	(1,100)	(2,800)	200
Return to provision	(500)	(3,700)	(500)
ACAP investment sale	0	20,200	0
Other items, net	(2,600)	3,300	4,800
Total income tax expense	$ 204,018	$ 152,900	$ 56,052
Rate Reconciliation, Percentage
Tax at federal statutory rate (as percent)	21.00%	21.00%	21.00%
State income tax, net of federal benefit (as percent)	1.80%	(1.20%)	(3.30%)
Change in uncertain tax positions (as percent)	5.10%	2.60%	4.40%
Foreign residual income (as percent)	4.60%	6.10%	27.80%
Nondeductible costs (as percent)	1.80%	2.90%	5.00%
Tax rate changes (as percent)	0.30%	0.20%	(1.50%)
Audit settlement (as percent)	0.10%	0.10%	0.90%
Income tax credits and incentive (as percent)	(6.50%)	(8.80%)	(31.90%)
Legal entity restructuring (as percent)	(2.20%)	0.00%	0.00%
Exclusion of tax on non-controlling interests (as percent)	(1.70%)	(1.70%)	(4.40%)
Valuation allowance (as percent)	(1.30%)	(1.80%)	7.80%
Tax exempt income (as percent)	(0.20%)	(0.40%)	(1.50%)
Foreign tax rate differential (as percent)	(0.10%)	(0.40%)	0.10%
Return to provision (as percent)	(0.10%)	(0.50%)	(0.20%)
ACAP investment sale (as percent)	0.00%	2.80%	0.00%
Other items, net (as percent)	(0.30%)	0.40%	2.10%
Total income tax expense (as percent)	22.30%	21.30%	26.30%