Income Taxes (Reconciliation of U.S Statutory Rate to Effective Tax Rate) (Details)	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Income Tax Disclosure [Abstract]
Statutory tax rate	21.00%	21.00%	21.00%
State income taxes, net of federal tax benefit	(0.50%)	0.30%	(0.10%)
Taxes on international activities	(0.10%)	(2.10%)	0.20%
Research credit	(3.10%)	(3.60%)	(3.30%)
Net excess income tax benefit from stock-based compensation	(4.20%)	(2.80%)	(3.50%)
Adjustments of prior period tax items	0.40%	1.00%	0.90%
Compensation and benefits	0.50%	0.40%	0.30%
Transition Tax			3.30%
Other items, net	1.10%	0.50%	0.20%
Effective tax rate	15.10%	14.70%	19.00%