Share-Based Payments (Narrative) (Details) - USD ($) $ / shares in Units, $ in Thousands, shares in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Maximum number of shares authorized for issuance (in shares)	17.9
Shares available for future awards (in shares)	4.6
Share-based compensation expense	$ 27,500	$ 23,900	$ 27,300
Tax benefit recognized for share-based compensation arrangements	$ 6,600	$ 5,700	$ 6,600
Share options granted (in shares)	0.1
RSE awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Anti-dilutive awards excluded from the calculation of diluted weighted-average shares outstanding (in shares)	0.0	0.2
Share options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period (in years)	3 years
Expiration period (in years)	10 years
Share options granted (in shares)	0.1	0.3
Compensation expense to be recognized over vesting period	$ 2,200	$ 4,600
Unrecognized compensation expense, share options	$ 3,200
Unrecognized compensation expense, weighted-average period to recognize (in years)	1 year 6 months
PSU awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense, weighted-average period to recognize (in years)	1 year 9 months 18 days
Unrecognized compensation expense, RSE awards	$ 9,900
Weighted-average grant date fair value, granted (in usd per share)	$ 58.55	$ 56.53	$ 29.25
Estimated fair value of vested awards	$ 62,090
RSE awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense, weighted-average period to recognize (in years)	2 years 3 months 18 days
Unrecognized compensation expense, RSE awards	$ 24,300
Weighted-average grant date fair value, granted (in usd per share)	$ 40.17	$ 42.49	$ 35.16
Estimated fair value of vested awards	$ 20,200	$ 15,400	$ 13,200