Income Taxes - Reconciliation of Federal Statutory Tax Rate to Company's Effective Tax Rate (Details)	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Income Tax Disclosure [Abstract]
Federal statutory tax rate	21.00%	21.00%	21.00%
State and local income taxes, net of federal tax benefit	(0.70%)	(1.00%)	(1.10%)
Foreign income tax at rates other than 21%	(9.10%)	(8.20%)	(7.30%)
Effect of foreign operations	4.30%	(3.90%)	5.60%
Effect of Research Credits, FDII and Other Credits (a)	(22.10%)	(3.20%)	(2.20%)
Effect of share-based compensation	(0.30%)	(0.40%)	(1.70%)
Effect of gain on divestitures	0.00%	3.20%	0.00%
Effect of valuation allowance	19.30%	0.00%	(5.50%)
Effect of nondeductible costs	2.20%	0.00%	0.00%
Other, net	0.40%	0.40%	(0.50%)
Total	15.00%	7.90%	8.30%