Income Taxes (Narrative) (Details) - USD ($)	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017
Income Tax Disclosures [Line Items]
Deferred Tax Assets, Operating Loss Carryforwards, Foreign	$ 40,500,000
Deferred tax assets related to domestic federal net operating loss carryforwards	21,600,000
Deferred tax assets related to state net operating loss carryforwards	7,600,000
Valuation Allowance, Deferred Tax Asset, Increase (Decrease), Amount	5,800,000
Valuation allowances on deferred tax assets	(50,800,000)	$ (45,000,000.0)
Impact of tax holidays	$ 3,300,000	$ 5,200,000	$ 4,300,000
Benefit of tax holidays on net income per share (diluted) (usd per share)	$ 0.05	$ 0.08	$ 0.06
Undistributed Earnings of Foreign Subsidiaries	$ 37,300,000
Amount of reasonably possible decrease	1,800,000
Total gross unrecognized tax benefits	3,900,000	$ 9,600,000	$ 6,200,000	$ 4,500,000
Unrecognized tax benefits that would impact effective tax rate, if recognized	3,500,000	9,300,000	5,600,000
Accrued interest and penalties related to unrecognized tax benefits	1,400,000	1,700,000	2,100,000
Income tax benefit for interest and penalties	400,000	500,000
Payment, Tax Withholding, Share-based Payment Arrangement	(16,500,000)	(4,700,000)	(14,100,000)
Deferred Tax Remeasurement, Amount	0	0	93,800,000
Transition tax obligation, amount	0	1,000,000.0	22,900,000
Deferred Tax Assets, State Taxes	23,900,000
Deferred Tax Assets, Capital Loss Carryforwards	1,100,000
Deferred tax asset, Lease Liabilities	18,800,000
Significant Change in Unrecognized Tax Benefits is Reasonably Possible [Line Items]
Income tax benefit for interest and penalties	400,000	500,000
Total gross unrecognized tax benefits	$ 3,900,000	$ 9,600,000	$ 6,200,000	$ 4,500,000