Revenue from Contracts with Customers - Revenue By Geographic Segment (Details) - USD ($) $ in Thousands		12 Months Ended
		Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Segment Reporting Revenue Reconciling Item [Line Items]
Total revenue		$ 2,298,472	$ 2,097,053	$ 1,933,347
Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Total revenue		2,298,472	2,097,053	1,933,347
Americas | Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Total revenue	[1]	1,087,929	1,023,273	895,095
Europe | Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Total revenue	[2]	859,387	753,796	714,216
Asia Pacific | Operating Segments
Segment Reporting Revenue Reconciling Item [Line Items]
Total revenue		$ 351,156	$ 319,984	$ 324,036

[1] Includes revenue in the United States totaling $1,057.3 million, $993.8 million, and $864.7 million for 2024, 2023 and 2022, respectively.

[2] Includes revenue in Germany totaling $330.5 million, $292.0 million, and $318.5 million for 2024, 2023 and 2022, respectively.