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Investments - Summary of Investments (Details) - USD ($) $ in Millions	Dec. 31, 2024	Sep. 30, 2024
Investment Holdings [Line Items]
Total investments, at fair value	$ 806.9	$ 838.0
Investments in equity method investees	1,175.5	1,219.7
Other investments	410.1	280.7
Investments	2,392.5	2,338.4
Sponsored funds and separate accounts [Member]
Investment Holdings [Line Items]
Investments, at fair value	469.1	509.1
Investments related to long-term incentive plans [Member]
Investment Holdings [Line Items]
Investments, at fair value	266.3	271.6
Other equity and debt investments [Member]
Investment Holdings [Line Items]
Investments, at fair value	$ 71.5	$ 57.3

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