Business combinations - Changes in Goodwill (Details) $ in Thousands  | 
6 Months Ended | 
|---|---|
| 
 Mar. 31, 2021  
USD ($) 
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| Goodwill [Roll Forward] | |
| Balance at the beginning of the period | $ 593,129 | 
| Estimated effects of acquisitions | 304,048 | 
| Foreign currency translation | 2,619 | 
| Balance at the end of the period | 899,796 | 
| U.S. Services | |
| Goodwill [Roll Forward] | |
| Balance at the beginning of the period | 164,472 | 
| Estimated effects of acquisitions | 0 | 
| Foreign currency translation | 0 | 
| Balance at the end of the period | 164,472 | 
| U.S. Federal Services | |
| Goodwill [Roll Forward] | |
| Balance at the beginning of the period | 381,719 | 
| Estimated effects of acquisitions | 303,465 | 
| Foreign currency translation | 0 | 
| Balance at the end of the period | 685,184 | 
| Outside the U.S. | |
| Goodwill [Roll Forward] | |
| Balance at the beginning of the period | 46,938 | 
| Estimated effects of acquisitions | 583 | 
| Foreign currency translation | 2,619 | 
| Balance at the end of the period | $ 50,140 | 
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- Definition Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized. Reference 1: http://www.xbrl.org/2003/role/disclosureRef 
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- Definition Amount of increase in asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized resulting from a business combination. Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef 
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- Definition Amount of foreign currency translation gain (loss) which increases (decreases) an asset representing future economic benefits from other assets acquired in a business combination that are not individually identified and separately recognized. Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef 
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- Definition A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period. No definition available. 
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