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Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Dec. 31, 2024 | Sep. 30, 2024
--- | --- | ---
Goodwill (not amortized) | $ 3,423,420 | $ 3,461,891
Intangible assets with finite lives (amortized), Gross Carrying Amount | 1,822,484 | 1,840,304
Intangible assets with finite lives (amortized), Accumulated Amortization | 950,376 | 942,828
Intangible assets with finite lives (amortized), Net Book Value | 872,108 | 897,476
Intangible Assets, Net (Including Goodwill) | 4,295,528 | 4,359,367
Purchased Software |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 628,414 | 634,439
Intangible assets with finite lives (amortized), Accumulated Amortization | 440,693 | 436,471
Intangible assets with finite lives (amortized), Net Book Value | 187,721 | 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 | 1,129,789 | 1,141,086
Intangible assets with finite lives (amortized), Accumulated Amortization | 460,818 | 457,718
Intangible assets with finite lives (amortized), Net Book Value | 668,971 | 683,368
Trademarks and Trade Names |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 37,565 | 37,961
Intangible assets with finite lives (amortized), Accumulated Amortization | 22,149 | 21,821
Intangible assets with finite lives (amortized), Net Book Value | 15,416 | 16,140
Other |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 3,839 | 3,941
Intangible assets with finite lives (amortized), Accumulated Amortization | 3,839 | 3,941
Intangible assets with finite lives (amortized), Net Book Value | $ 0 | $ 0

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