Other Balance Sheet Items (Tables)
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3 Months Ended | 
Dec. 31, 2022  | 
| Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents [Abstract] | 
 
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| Schedule of Cash and Cash Equivalents | 
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| Table 9.1: Details of Cash and Cash Equivalents and Restricted Cash |  
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December 31, 2022 | 
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September 30, 2022 | 
 
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(in thousands) | 
 
| Cash and cash equivalents | 
$ | 
63,050  | 
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$ | 
40,658  | 
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| Restricted cash (1) | 
96,777  | 
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 | 
96,137  | 
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| Cash, cash equivalents, and restricted cash | 
$ | 
159,827  | 
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$ | 
136,795  | 
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 (1)Restricted cash is recorded within "Prepaid expenses and other current assets" on the Consolidated Balance Sheets. At December 31, 2022 and September 30, 2022, this balance includes $52.3 million and $60.7 million, respectively, 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". The majority of the remaining balance are funds held in trust on behalf of certain clients; this asset is similarly offset with a corresponding liability in "Other current liabilities".
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| Restrictions on Cash and Cash Equivalents | 
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| Table 9.1: Details of Cash and Cash Equivalents and Restricted Cash |  
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December 31, 2022 | 
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September 30, 2022 | 
 
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(in thousands) | 
 
| Cash and cash equivalents | 
$ | 
63,050  | 
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$ | 
40,658  | 
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| Restricted cash (1) | 
96,777  | 
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 | 
96,137  | 
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| Cash, cash equivalents, and restricted cash | 
$ | 
159,827  | 
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$ | 
136,795  | 
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 (1)Restricted cash is recorded within "Prepaid expenses and other current assets" on the Consolidated Balance Sheets. At December 31, 2022 and September 30, 2022, this balance includes $52.3 million and $60.7 million, respectively, 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". The majority of the remaining balance are funds held in trust on behalf of certain clients; this asset is similarly offset with a corresponding liability in "Other current liabilities".
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| Supplementary Cash Flow Information | 
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| Table 9.2: Supplemental Disclosures of Cash Flow Information |  
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For the Three Months Ended | 
 
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December 31, 2022 | 
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December 31, 2021 | 
 
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(in thousands) | 
 
| Interest payments | 
$ | 
19,748  | 
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$ | 
8,943  | 
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| Income tax payments | 
$ | 
4,982  | 
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$ | 
8,009  | 
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| Details of Accounts Receivable | 
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| Table 9.3: Details of Accounts Receivable, Net |  
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December 31, 2022 | 
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September 30, 2022 | 
 
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(in thousands) | 
 
| Billed and billable receivables | 
$ | 
879,851  | 
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$ | 
723,979  | 
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| Unbilled receivables | 
142,844  | 
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 | 
91,404  | 
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| Allowance for credit losses | 
(8,649) | 
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(8,273) | 
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| Accounts receivable, net | 
$ | 
1,014,046  | 
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$ | 
807,110  | 
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