Income Taxes (Narrative) (Details) - USD ($)	12 Months Ended
	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017	Oct. 01, 2018	Oct. 01, 2017	Sep. 30, 2016
Income Tax Disclosure [Line Items]
Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent	21.00%	25.00%	(35.00%)
Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Amount	$ 26,952,000	$ 38,743,000	$ 27,932,000
Decrease of valuation allowance in foreign jurisdictions			9,000,000.0
Foreign tax on U.S. provision	6,547,000	$ 2,736,000	2,737,000
Effective Income Tax Rate Reconciliation, Prior Year Income Taxes, Percent		24.50%
Income taxes payable	23,400,000	$ 24,200,000
Provision (benefit) from deferred income taxes	1,708,000	(56,556,000)	(28,289,000)
Accrued income taxes	17,400,000	18,000,000.0
Prepaid income taxes	5,300,000	4,800,000
Income tax payments	38,900,000	22,600,000	35,400,000
Total stockholders’ equity	1,201,998,000	874,589,000	885,436,000			$ 842,666,000
Deferred tax assets	198,634,000	165,566,000
Non-U.S. tax credit carryforwards	0	2,201,000
Gross Deferred Interest Carryforward	86,900,000
Gross Deferred Amortization Carryforward	825,900,000
Valuation allowance	177,663,000	141,950,000	279,700,000			235,500,000
Interest Expense	43,047,000	41,673,000	42,400,000
Penalty expense	0	0	0
Interest expense related to income tax accruals	500,000
Accrued tax penalties	0	0	0
Income tax provision upon recognition of unrecognized tax benefit	11,500,000
Unrecognized tax benefits, increase in valuation allowance upon recognition	5,400,000
Potential decrease in unrecognized tax benefits	500,000
Stock-based compensation	86,400,000	82,939,000	76,708,000
Tax benefit recognition related to stock based compensation	16,600,000	28,300,000	1,300,000
Provision (benefit) for income taxes	47,760,000	(23,331,000)	(7,645,000)
Realignment [Member]
Income Tax Disclosure [Line Items]
Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Amount		24,000,000	28,000,000
Domestic Country [Member]
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	8,800,000
Valuation allowance	146,100,000
Domestic Country [Member] | Research Tax Credit Carryforward [Member]
Income Tax Disclosure [Line Items]
Credit carryforwards	26,200,000
State - Massachusetts [Member]
Income Tax Disclosure [Line Items]
Income taxes payable		1,700,000
State - Massachusetts [Member] | Research Tax Credit Carryforward [Member]
Income Tax Disclosure [Line Items]
Credit carryforwards	22,100,000
Foreign Country [Member]
Income Tax Disclosure [Line Items]
Net operating loss carryforwards	64,400,000
Non-U.S. tax credit carryforwards	3,200,000
Valuation allowance	31,600,000
Windfall Tax Benefit [Member]
Income Tax Disclosure [Line Items]
Provision (benefit) for income taxes	6,700,000	13,200,000
Patents [Member]
Income Tax Disclosure [Line Items]
Foreign tax on U.S. provision		2,700,000	2,000,000.0
Net Decrease in Deferred Tax Liability [Member]
Income Tax Disclosure [Line Items]
Provision (benefit) from deferred income taxes		14,100,000
Accounting Standards Update 2016-16 [Member]
Income Tax Disclosure [Line Items]
Deferred tax assets				$ 75,300,000
Other Tax Assets				6,000,000.0
Other Tax Liabilities				3,000,000.0
Accounting Standards Update 2016-09 [Member]
Income Tax Disclosure [Line Items]
Windfall tax deductions not yet recognized					$ 37,000,000.0
Windfall Tax Deductions Not Yet Recognized Offset Valuation Allowance					$ 36,900,000
Other Current Liabilities [Member]
Income Tax Disclosure [Line Items]
Accrued income taxes	400,000	1,800,000
Other Liabilities [Member]
Income Tax Disclosure [Line Items]
Accrued income taxes	5,600,000	4,400,000
Additional Paid-in Capital [Member] | Windfall Tax Benefit [Member]
Income Tax Disclosure [Line Items]
Provision (benefit) for income taxes			600,000
income tax expense [Member]
Income Tax Disclosure [Line Items]
Interest Expense	100,000	600,000	900,000
Accumulated Deficit [Member]
Income Tax Disclosure [Line Items]
Total stockholders’ equity	(191,390,000)	$ (599,409,000)	$ (650,840,000)			$ (657,079,000)
Accumulated Deficit [Member] | Accounting Standards Update 2016-16 [Member]
Income Tax Disclosure [Line Items]
Total stockholders’ equity				$ 72,300,000
Paid in 2017 [Member] | Korea
Income Tax Disclosure [Line Items]
Income Tax Examination, Estimate of Possible Loss	12,000,000
Additional Exposure [Member] | Korea
Income Tax Disclosure [Line Items]
Income Tax Examination, Estimate of Possible Loss	$ 13,000,000