Goodwill and Acquired Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2023
Goodwill (not amortized)	$ 3,493,316	$ 3,461,891	$ 3,358,511
Intangible assets with finite lives (amortized), Gross Carrying Amount	1,853,441	1,840,304
Intangible assets with finite lives (amortized), Accumulated Amortization	1,028,778	942,828
Intangible assets with finite lives (amortized), Net Book Value	824,663	897,476
Intangible Assets, Net (Including Goodwill)	4,317,979	4,359,367
Purchased Software
Intangible assets with finite lives (amortized), Gross Carrying Amount	639,104	634,439
Intangible assets with finite lives (amortized), Accumulated Amortization	472,357	436,471
Intangible assets with finite lives (amortized), Net Book Value	166,747	197,968
Capitalized Software
Intangible assets with finite lives (amortized), Gross Carrying Amount	22,877	22,877
Intangible assets with finite lives (amortized), Accumulated Amortization	22,877	22,877
Intangible assets with finite lives (amortized), Net Book Value	0	0
Customer Lists and Relationships
Intangible assets with finite lives (amortized), Gross Carrying Amount	1,149,262	1,141,086
Intangible assets with finite lives (amortized), Accumulated Amortization	505,202	457,718
Intangible assets with finite lives (amortized), Net Book Value	644,060	683,368
Trademarks and Trade Names
Intangible assets with finite lives (amortized), Gross Carrying Amount	38,179	37,961
Intangible assets with finite lives (amortized), Accumulated Amortization	24,323	21,821
Intangible assets with finite lives (amortized), Net Book Value	13,856	16,140
Other
Intangible assets with finite lives (amortized), Gross Carrying Amount	4,019	3,941
Intangible assets with finite lives (amortized), Accumulated Amortization	4,019	3,941
Intangible assets with finite lives (amortized), Net Book Value	$ 0	$ 0