Goodwill and Acquired Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Goodwill (not amortized)	$ 3,461,891	$ 3,358,511	$ 2,353,654
Intangible assets with finite lives (amortized), Gross Carrying Amount	1,840,304	1,795,627
Intangible assets with finite lives (amortized), Accumulated Amortization	942,828	854,378
Intangible assets with finite lives (amortized), Net Book Value	897,476	941,249
Intangible Assets, Net (Including Goodwill)	4,359,367	4,299,760
Purchased Software
Intangible assets with finite lives (amortized), Gross Carrying Amount	634,439	615,915
Intangible assets with finite lives (amortized), Accumulated Amortization	436,471	395,109
Intangible assets with finite lives (amortized), Net Book Value	197,968	220,806
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	1,141,086	1,116,117
Intangible assets with finite lives (amortized), Accumulated Amortization	457,718	413,125
Intangible assets with finite lives (amortized), Net Book Value	683,368	702,992
Trademarks and Trade Names
Intangible assets with finite lives (amortized), Gross Carrying Amount	37,961	36,851
Intangible assets with finite lives (amortized), Accumulated Amortization	21,821	19,400
Intangible assets with finite lives (amortized), Net Book Value	16,140	17,451
Other
Intangible assets with finite lives (amortized), Gross Carrying Amount	3,941	3,867
Intangible assets with finite lives (amortized), Accumulated Amortization	3,941	3,867
Intangible assets with finite lives (amortized), Net Book Value	$ 0	$ 0