Employee Benefit Plans - Time-Based Restricted Stock Unit Equity Awards (Details) - Restricted Stock Units (RSUs) [Member] $ / shares in Units, $ in Millions	12 Months Ended
	Sep. 30, 2023 USD ($) grant_recipient $ / shares shares	Sep. 30, 2022 USD ($) grant_recipient $ / shares shares	Sep. 30, 2021 USD ($) grant_recipient $ / shares shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested in Period, Fair Value | $	$ 115.2	$ 120.1	$ 131.3
Number of Restricted Stock Units
Outstanding at beginning of year, shares | shares	3,466,094	3,817,265	4,725,701
Granted, shares | shares	877,131	1,153,124	856,615
Vested, shares | shares	(1,251,785)	(1,402,642)	(1,644,263)
Cancelled, shares | shares	(124,515)	(101,653)	(120,788)
Outstanding at end of year, shares | shares	2,966,925	3,466,094	3,817,265
Weighted Average Grant Date Fair Value
Outstanding at beginning of year, weighted average grant date fair value, per share | $ / shares	$ 57.50	$ 46.16	$ 34.79
Granted, weighted average grant date fair value, per share | $ / shares	93.44	74.96	83.13
Vested, weighted average grant date fair value, per share | $ / shares	50.61	41.44	33.26
Cancelled, weighted average grant date fair value, per share | $ / shares	61.95	51.22	39.16
Outstanding at end of year, weighted average grant date fair value, per share | $ / shares	$ 70.85	$ 57.50	$ 46.16
Additional information - restricted stock units
Share-based compensation expense | $	$ 65.7	$ 63.6	$ 56.5
Unrecognized compensation expense | $	$ 156.4
Weighted average period over which unrecognized compensation cost is expected to be recognized	2 years 7 months 6 days
Minimum [Member]
Additional information - restricted stock units
Vesting period	3 years
Maximum [Member]
Additional information - restricted stock units
Vesting period	5 years
Fiscal 2021 Grant
Additional information - restricted stock units
RSU grant recipients | grant_recipient			1,030
Fiscal 2022 Grant
Additional information - restricted stock units
RSU grant recipients | grant_recipient		1,200
Fiscal 2023 Grant
Additional information - restricted stock units
RSU grant recipients | grant_recipient	1,380