| Other Balance Sheet Items (Tables)
 | 6 Months Ended | 
| Mar. 31, 2023 | 
|---|
| Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents [Abstract] |  | 
| Schedule of Cash and Cash Equivalents | 
(1)Restricted cash is recorded within "Prepaid expenses and other current assets" on the Consolidated Balance Sheets. At September 30, 2022, this balance included $60.7 million of funds received from a customer which had previously been sold under our Receivables Purchase Agreement; this is offset by a corresponding liability in "Other current liabilities". No similar arrangements existed at March 31, 2023. The remaining balance includes funds held in trust on behalf of certain clients, offset with a corresponding liability in "Other current liabilities", and certain collateral obligations on contracts.
|  |  |  |  |  |  |  |  |  |  |  |  |  | Table 10.1: Details of Cash and Cash Equivalents and Restricted Cash |  
|  | March 31, 2023 |  | September 30, 2022 |  
|  | (in thousands) |  
| Cash and cash equivalents | $ | 56,344 |  |  | $ | 40,658 |  |  
| Restricted cash (1) | 62,376 |  |  | 96,137 |  |  
| Cash, cash equivalents, and restricted cash | $ | 118,720 |  |  | $ | 136,795 |  |  | 
| Schedule of Restrictions on Cash and Cash Equivalents | 
(1)Restricted cash is recorded within "Prepaid expenses and other current assets" on the Consolidated Balance Sheets. At September 30, 2022, this balance included $60.7 million of funds received from a customer which had previously been sold under our Receivables Purchase Agreement; this is offset by a corresponding liability in "Other current liabilities". No similar arrangements existed at March 31, 2023. The remaining balance includes funds held in trust on behalf of certain clients, offset with a corresponding liability in "Other current liabilities", and certain collateral obligations on contracts.
|  |  |  |  |  |  |  |  |  |  |  |  |  | Table 10.1: Details of Cash and Cash Equivalents and Restricted Cash |  
|  | March 31, 2023 |  | September 30, 2022 |  
|  | (in thousands) |  
| Cash and cash equivalents | $ | 56,344 |  |  | $ | 40,658 |  |  
| Restricted cash (1) | 62,376 |  |  | 96,137 |  |  
| Cash, cash equivalents, and restricted cash | $ | 118,720 |  |  | $ | 136,795 |  |  | 
| Schedule of Supplementary Cash Flow Information | 
|  |  |  |  |  |  |  |  |  |  |  |  |  | Table 10.2: Supplemental Disclosures of Cash Flow Information |  
|  | For the Six Months Ended |  
|  | March 31, 2023 |  | March 31, 2022 |  
|  | (in thousands) |  
| Interest payments | $ | 19,262 |  |  | $ | 17,755 |  |  
| Income tax payments | $ | 31,926 |  |  | $ | 50,531 |  |  | 
| Schedule of Details of Accounts Receivable | 
|  |  |  |  |  |  |  |  |  |  |  |  |  | Table 10.3: Details of Accounts Receivable, Net |  
|  | March 31, 2023 |  | September 30, 2022 |  
|  | (in thousands) |  
| Billed and billable receivables | $ | 614,907 |  |  | $ | 723,979 |  |  
| Unbilled receivables | 134,695 |  |  | 91,404 |  |  
| Allowance for credit losses | (7,215) |  |  | (8,273) |  |  
| Accounts receivable, net | $ | 742,387 |  |  | $ | 807,110 |  |  |