Income Taxes - Schedule of Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Thousands	Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Deferred Tax Assets, Net [Abstract]
Net operating loss carryforwards	$ 12,074	$ 14,141
Foreign tax credits	5,996	2,028
Capitalized research and development	176,610	136,001
Pension benefits	6,868	7,629
Prepaid expenses	22,391	18,551
Deferred revenue	2,970	2,607
Stock-based compensation	23,514	22,231
Other reserves not currently deductible	39,888	34,422
Amortization of intangible assets	36,560	60,527
Research and development and other tax credits	8,984	25,706
Lease liabilities	43,650	46,460
Fixed assets	114,109	106,741
Capital loss carryforward	4,517	3,875
Other	5,608	3,528
Gross deferred tax assets	503,739	484,447
Valuation allowance	(8,529)	(21,755)	$ (21,695)	$ (22,283)
Total deferred tax assets	495,210	462,692
Deferred Tax Liabilities, Net [Abstract]
Acquired intangible assets not deductible	(246,107)	(257,731)
Lease assets	(29,298)	(34,160)
Pension prepayments	(4,279)	(3,283)
Deferred revenue	(10,212)	(1,243)
Depreciation	(3,277)	(4,683)
Deferred income	(14,518)	(11,636)
Prepaid commissions	(14,479)	(13,738)
Other	(9,120)	(9,030)
Total deferred tax liabilities	(331,290)	(335,504)
Net deferred tax assets	$ 163,920	$ 127,188