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Segment and Geographic Information - Revenue By Product Segment (Details) - USD ($)
$ in Thousands
 12 Months Ended
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2018
Total revenue $ 1,458,415 $ 1,255,631 $ 1,241,824
Operating Segments      
Total revenue 1,458,415 1,255,631 1,241,824
Calculated under Revenue Guidance in Effect before Topic 606      
Total revenue   1,311,494 1,241,824
Calculated under Revenue Guidance in Effect before Topic 606 | Operating Segments      
Total revenue   1,311,494  
Core Group | Operating Segments      
Total revenue 1,025,668 868,970 895,149
Core Group | Calculated under Revenue Guidance in Effect before Topic 606 | Operating Segments      
Total revenue   921,386  
Growth Group | Operating Segments      
Total revenue 222,646 167,544 139,278
Growth Group | Calculated under Revenue Guidance in Effect before Topic 606 | Operating Segments      
Total revenue   175,619  
Focused Solutions Group | Operating Segments      
Total revenue $ 210,101 219,117 $ 207,397
Focused Solutions Group | Calculated under Revenue Guidance in Effect before Topic 606 | Operating Segments      
Total revenue   $ 214,489