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Goodwill and Other Intangible Assets - Narrative (Details) - USD ($) | 3 Months Ended | 12 Months Ended
--- | --- | ---
Mar. 31, 2024 | Sep. 30, 2023 | Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Goodwill and intangible asset impairment | $ 0 |  |  |  |
Goodwill impairment |  |  | $ 0 | $ 157,500,000 | $ 0
Goodwill |  | $ 3,529,200,000 | 3,993,300,000 | 3,529,200,000 | 3,524,000,000
Amortization of intangible assets |  |  | 155,000,000.0 | 116,600,000 | 112,300,000
Estimated amortization expense in 2025 |  |  | 151,400,000 |  |
Estimated amortization expense in 2026 |  |  | 148,900,000 |  |
Estimated amortization expense in 2027 |  |  | 140,700,000 |  |
Estimated amortization expense in 2028 |  |  | 128,400,000 |  |
Estimated amortization expense in 2029 |  |  | 88,700,000 |  |
Sensia |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Reporting unit, carrying value |  | 665,100,000 |  | 665,100,000 |
Goodwill impairment |  | $ 157,500,000 |  |  |
Goodwill |  |  | 160,700,000 |  |
Software products |  |  |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |  |  |
Amortization of intangible assets |  |  | $ 11,600,000 | $ 11,300,000 | $ 9,400,000

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