Income Taxes - Schedule of Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Thousands	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Deferred Tax Assets, Net [Abstract]
Net operating loss carryforwards	$ 22,272	$ 40,419
Foreign tax credits	3,750	14,527
Capitalized research and development	83,748	23,274
Pension benefits	5,327	7,639
Prepaid expenses	15,040	15,886
Deferred revenue	5,902	2,146
Stock-based compensation	19,684	19,486
Other reserves not currently deductible	19,604	14,689
Amortization of intangible assets	90,888	130,825
Research and development and other tax credits	64,618	78,862
Lease liabilities	50,102	46,672
Fixed assets	83,796	78,249
Capital loss carryforward	3,700	3,955
Other	2,279	1,256
Gross deferred tax assets	470,710	477,885
Valuation allowance	(21,695)	(22,283)	$ (52,085)	$ (205,423)
Total deferred tax assets	449,015	455,602
Deferred Tax Liabilities, Net [Abstract]
Acquired intangible assets not deductible	(263,178)	(118,360)
Lease assets	(37,332)	(36,940)
Pension prepayments	(1,808)	(2,622)
Deferred revenue	(17,400)	(35,193)
Depreciation	(5,779)	(6,937)
Deferred income	(8,656)	(5,991)
Prepaid commissions	(13,757)	(13,356)
Other	(7,294)	(8,508)
Total deferred tax liabilities	(355,204)	(227,907)
Net deferred tax assets	$ 93,811	$ 227,695