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Goodwill and Intangibles - Schedule of Acquired Intangibles in Accompanying Consolidated Balance Sheets (Details)
$ in Thousands
9 Months Ended
Jun. 30, 2023
USD ($)
Finite-lived Intangible Assets [Roll Forward]  
Beginning balance $ 1,394,052
Amortization (152,232)
Acquired 5,537
Post-Acquisition Adjustments (1,409)
Foreign currency translation and other 108,729
Ending balance 1,354,677
Customer Relationships, Contracts and Backlog  
Finite-lived Intangible Assets [Roll Forward]  
Beginning balance 1,136,438
Amortization (132,772)
Acquired 5,537
Post-Acquisition Adjustments (1,409)
Foreign currency translation and other 83,415
Ending balance 1,091,209
Developed Technology  
Finite-lived Intangible Assets [Roll Forward]  
Beginning balance 88,931
Amortization (11,720)
Acquired 0
Post-Acquisition Adjustments 0
Foreign currency translation and other 1,785
Ending balance 78,996
Trade Names  
Finite-lived Intangible Assets [Roll Forward]  
Beginning balance 168,683
Amortization (7,740)
Acquired 0
Post-Acquisition Adjustments 0
Foreign currency translation and other 23,529
Ending balance $ 184,472