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Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Thousands | 3 Months Ended | 9 Months Ended
--- | --- | ---
Jun. 30, 2019 | Jun. 30, 2018 | Jun. 30, 2019 | Jun. 30, 2018
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | $ 730,710 | $ 597,855 | $ 2,131,849 | $ 1,833,790
United States of America |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 583,428 |  | 1,675,101 |
United Kingdom |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 72,265 |  | 224,017 |
Australia |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 48,744 |  | 153,114 |
Rest of world |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 26,273 |  | 79,617 |
Total U.S. state government agencies |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 294,567 |  | 872,909 |
New York State government agencies |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 90,295 |  | 271,865 |
Other U.S. state government agencies |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 204,272 |  | 601,044 |
United States Federal Government agencies |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 276,294 |  | 745,195 |
International government agencies |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 136,848 |  | 425,921 |
Other, including local municipalities and commercial customers |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 23,001 |  | 87,824 |
Performance-based |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 260,052 |  | 834,531 |
Cost-plus |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 282,795 |  | 756,227 |
Fixed price |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 142,940 |  | 429,962 |
Time and materials |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 44,923 |  | 111,129 |
U.S. Health & Human Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 291,132 |  | 876,082 |
U.S. Federal Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 292,295 |  | 799,018 |
Outside the United States |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 147,283 |  | 456,749 |
Program administration | U.S. Health & Human Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 212,638 |  | 651,343 |
Program administration | U.S. Federal Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 204,622 |  | 554,739 |
Program administration | Outside the United States |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 16,767 |  | 48,009 |
Assessments and appeals | U.S. Health & Human Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 35,657 |  | 106,209 |
Assessments and appeals | U.S. Federal Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 47,679 |  | 127,409 |
Assessments and appeals | Outside the United States |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 62,152 |  | 192,233 |
Workforce and children services | U.S. Health & Human Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 29,146 |  | 76,947 |
Workforce and children services | Outside the United States |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 65,819 |  | 208,856 |
Other | U.S. Health & Human Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 13,691 |  | 41,583 |
Other | Outside the United States |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 2,545 |  | 7,651 |
Technology solutions | U.S. Federal Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | $ 39,994 |  | $ 116,870 |

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