Income Taxes (Narrative) (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2018	Sep. 30, 2017	Sep. 30, 2016	Oct. 01, 2017	Sep. 30, 2015
Income Tax Disclosure [Line Items]
Effective Income Tax Rate Reconciliation, Prior Year Income Taxes, Percent	24.50%
Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Amount	$ (38,743)	$ (27,932)	$ (27,513)
Decrease of valuation allowance in foreign jurisdictions		(9,000)	(3,100)
Effective Income Tax Rate Reconciliation, Foreign Income Tax Withholding, Amount	2,736	2,737	1,987
Income taxes payable	24,200	16,200
Accrued income taxes	18,000	5,700
Other current liabilities	1,800	2,300
Prepaid income taxes	4,800	7,100
Other liabilities	4,400	8,200
Income tax payments	22,600	35,400	25,500
Deferred Tax Assets, Tax Credit Carryforwards, Foreign	2,201	21,099
Gross Deferred Interest Carryforward	104,500
Gross Deferred Amortization Carryforward	709,300
Valuation allowance	141,950	279,683	235,500		$ 198,200
Interest expense	600	900	500
Penalty expense	0	0	0
Interest expense related to income tax accruals	500	1,100
Accrued tax penalties	0	0	0
Unrecognized tax benefit	9,800	14,800	15,500		$ 14,100
Income tax provision upon recognition of unrecognized tax benefit	9,800
Unrecognized tax benefits, increase in valuation allowance upon recognition	3,700
Potential decrease in unrecognized tax benefits	2,000
Stock-based compensation	82,939	76,708	65,996
Tax benefit recognition related to stock based compensation	28,300	1,300	700
Increase (decrease) in income taxes payable	(10,323)	798	$ (6,749)
Deferred Tax Liability Not Recognized, Description of Temporary Difference, Undistributed Earnings of Foreign Subsidiaries	$ 0	$ (11,440)
Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent	25.00%	35.00%	35.00%
Benefit from deferred income taxes	$ (56,556)	$ (28,289)	$ (44,182)
Realignment [Member]
Income Tax Disclosure [Line Items]
Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Amount	(24,000)	(28,000)	(28,000)
Domestic Country [Member]
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	4,100
Deferred Tax Assets, Tax Credit Carryforwards, Foreign	2,200
Valuation allowance	108,600
Domestic Country [Member] | Research Tax Credit Carryforward [Member]
Income Tax Disclosure [Line Items]
Credit carryforwards	30,000
State - Massachusetts [Member] | Research Tax Credit Carryforward [Member]
Income Tax Disclosure [Line Items]
Credit carryforwards	22,400
Foreign Country [Member]
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	84,200
Credit carryforwards	5,000
Valuation allowance	33,300
Korea
Income Tax Disclosure [Line Items]
Income Tax Examination, Estimate of Possible Loss	12,000
Windfall Tax Benefit [Member]
Income Tax Disclosure [Line Items]
Increase (decrease) in income taxes payable	13,200	600	100
Patents [Member]
Income Tax Disclosure [Line Items]
Effective Income Tax Rate Reconciliation, Foreign Income Tax Withholding, Amount	2,700	$ 2,000	$ 2,000
US Tax on Undistributed Foreign Earnings [Member]
Income Tax Disclosure [Line Items]
Current Federal, State and Local, Tax Expense (Benefit)	2,100
Net Decrease in Deferred Tax Liability [Member]
Income Tax Disclosure [Line Items]
Benefit from deferred income taxes	$ 14,100
Accounting Standards Update 2016-09 [Member]
Income Tax Disclosure [Line Items]
Windfall tax deductions not yet recognized				$ 37,000
Windfall Tax Deductions Not Yet Recognized Offset Valuation Allowance				$ 36,900