Stockholders' Equity (Narrative) (Details) - USD ($) $ / shares in Units, $ in Thousands			1 Months Ended	12 Months Ended
	Jan. 25, 2023	Jan. 31, 2022	Nov. 30, 2019	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021	Jan. 22, 2022
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Total unrecognized compensation cost related to non-vested stock-based compensation arrangements				$ 21,104
Forfeiture rate, Board of Directors				0.00%
Forfeiture rate, non-Board of Directors				7.30%
Stock-based compensation expense, before tax				$ 23,958	$ 20,109	$ 21,475
Unrecognized compensation cost is expected to be recognized over a weighted-average period				8 months 8 days
Executive Separation and Release Agreement [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Stock-based compensation expense, before tax				$ 1,265
2017 Plan [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Number of additional shares available for future grants	500,000
Restricted Stock Units (RSUs) [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Vesting period, in years				4 years
Vesting rate				25.00%
Stock Options [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Vesting period, in years				4 years
Vested contractual term, in years				10 years
Exercise prices of stock options outstanding				$ 80.48	$ 74.40
Weighted-average exercise price				$ 84.84
Stock Options [Member] | ShareBasedC ompensation Award Tranche One [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Vesting rate				25.00%
2017 Authorization [Member] | 2017 Plan [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Number of shares available for future grants				2,689
2019 Authorization [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Stock repurchase program authorized amount					$ 26,742	$ 45,860
Repurchase period in years			3 years
Stock repurchase program, number of shares authorized to be repurchased					233,000	404,000
Stock repurchase program, number of shares authorized to be repurchased in-transit						110,000
Stock repurchase program authorized in-transit amount						$ 12,516
2022 Authorization [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Stock repurchase program authorized amount				$ 126,380	$ 446,042
Repurchase period in years		2 years
Stock repurchase program, number of shares authorized to be repurchased				1,060,000	3,890
Maximum [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Exercise prices of stock options outstanding				$ 117.64
Maximum [Member] | 2019 Authorization [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Stock repurchase program authorized amount			$ 500,000
Maximum [Member] | 2022 Authorization [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Stock repurchase program authorized amount							$ 800,000
Minimum [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Exercise prices of stock options outstanding				$ 40.26