Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Mar. 31, 2025	Sep. 30, 2024
Goodwill	$ 3,444,104	$ 3,461,891
Intangible assets with finite lives, Gross Carrying Amount	1,832,101	1,840,304
Intangible assets with finite lives, Accumulated Amortization	976,307	942,828
Intangible assets with finite lives, Net Book Value	855,794	897,476
Intangible Assets, Net (Including Goodwill)	4,299,898	4,359,367
Purchased Software
Intangible assets with finite lives, Gross Carrying Amount	631,889	634,439
Intangible assets with finite lives, Accumulated Amortization	451,196	436,471
Intangible assets with finite lives, Net Book Value	180,693	197,968
Capitalized Software
Intangible assets with finite lives, Gross Carrying Amount	22,877	22,877
Intangible assets with finite lives, Accumulated Amortization	22,877	22,877
Intangible assets with finite lives, Net Book Value	0	0
Customer Lists and Relationships
Intangible assets with finite lives, Gross Carrying Amount	1,135,655	1,141,086
Intangible assets with finite lives, Accumulated Amortization	475,455	457,718
Intangible assets with finite lives, Net Book Value	660,200	683,368
Trademarks and Trade Names
Intangible assets with finite lives, Gross Carrying Amount	37,780	37,961
Intangible assets with finite lives, Accumulated Amortization	22,879	21,821
Intangible assets with finite lives, Net Book Value	14,901	16,140
Other
Intangible assets with finite lives, Gross Carrying Amount	3,900	3,941
Intangible assets with finite lives, Accumulated Amortization	3,900	3,941
Intangible assets with finite lives, Net Book Value	$ 0	$ 0