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