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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 |

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