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Goodwill and Other Intangible Assets - Narrative (Details)	3 Months Ended	12 Months Ended
	Mar. 31, 2021 USD ($)	Sep. 30, 2021 USD ($) segment	Sep. 30, 2020 USD ($)	Sep. 30, 2019 USD ($)
Finite-Lived Intangible Assets [Line Items]
Number of operating segments \| segment		3
Goodwill and intangible asset impairment	$ 0
Amortization of intangible assets		$ 65,900,000	$ 50,200,000	$ 26,000,000.0
Estimated amortization expense in 2022		112,000,000
Estimated amortization expense in 2023		110,600,000
Estimated amortization expense in 2024		107,600,000
Estimated amortization expense in 2025		105,300,000
Estimated amortization expense in 2026		103,700,000
Software products
Finite-Lived Intangible Assets [Line Items]
Amortization of intangible assets		$ 11,900,000	$ 10,200,000	$ 10,400,000