Basis of Presentation and Accounting Policies - Narrative (Details) shares in Millions			3 Months Ended		6 Months Ended
	Apr. 20, 2020 USD ($)	Oct. 01, 2019 USD ($)	Mar. 31, 2020 USD ($) shares	Mar. 31, 2019 shares	Mar. 31, 2020 USD ($)	Mar. 31, 2019 USD ($)	Sep. 30, 2019 USD ($)
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Allowance for doubtful accounts			$ 20,700,000		$ 20,700,000		$ 17,400,000
Allowance for certain customer returns, rebates and incentives			$ 9,300,000		9,300,000		$ 12,400,000
Antidilutive share-based compensation awards (in shares) | shares			2.3	1.8
Capital expenditures in accounts payable or other current liabilities at period end					18,500,000	$ 11,100,000
Outstanding purchase of common stock recorded in accounts payable					2,000,000.0	$ 11,900,000
Operating lease right-of-use assets			$ 318,500,000		318,500,000
Operating lease liability			$ 341,900,000		$ 341,900,000
Accounting Standards Update 2016-02
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Operating lease right-of-use assets		$ 316,000,000
Operating lease liability		329,000,000
Accumulated other comprehensive loss | Accounting Standards Update 2016-02
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Reclassification from AOCI to retained earnings		$ 146,800,000
Subsequent Event | Note Payable
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Long-term debt issued	$ 400,000,000
Debt instrument, term	364 days
Ratio of EBITDA to interest expense	3.0
Subsequent Event | Notes
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Borrowing capacity	$ 1,250,000,000