Revenue from Contracts with Customers - Revenue By Geographic Segment (Details) - USD ($) $ in Thousands		12 Months Ended
		Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Segment Reporting Revenue Reconciling Item [Line Items]
Total revenue		$ 2,097,053	$ 1,933,347	$ 1,807,159
Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Total revenue		2,097,053	1,933,347	1,807,159
Americas | Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Total revenue	[1]	1,023,273	895,095	766,021
Europe | Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Total revenue	[2]	753,796	714,216	722,977
Asia Pacific | Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Total revenue		$ 319,984	$ 324,036	$ 318,161

[1] Includes revenue in the United States totaling $993.8 million, $864.7 million, and $741.3 million for 2023, 2022 and 2021, respectively.

[2] Includes revenue in Germany totaling $292.0 million, $318.5 million, and $290.7 million for 2023, 2022 and 2021, respectively.