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Goodwill and Acquired Intangible Assets (Goodwill and Acquired Intangible Assets) (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Goodwill (not amortized), Net Book Value $ 1,238,179 $ 1,182,457 $ 1,182,772
Intangible assets with finite lives (amortized), Gross Carrying Amount 778,968 766,199  
Intangible assets with finite lives (amortized), Accumulated Amortization 609,019 565,997  
Intangible assets with finite lives (amortized), Net Book Value 169,949 200,202  
Intangible Assets, Net (Including Goodwill) 1,408,128 1,382,659  
Purchased Software [Member]      
Intangible assets with finite lives (amortized), Gross Carrying Amount 377,359 362,679  
Intangible assets with finite lives (amortized), Accumulated Amortization 278,144 254,059  
Intangible assets with finite lives (amortized), Net Book Value $ 99,215 108,620  
Weighted average useful lives (in years) 9 years    
Capitalized Software [Member]      
Intangible assets with finite lives (amortized), Gross Carrying Amount $ 22,877 22,877  
Intangible assets with finite lives (amortized), Accumulated Amortization 22,877 22,877  
Intangible assets with finite lives (amortized), Net Book Value 0 0  
Customer Lists [Member]      
Intangible assets with finite lives (amortized), Gross Carrying Amount 355,931 357,586  
Intangible assets with finite lives (amortized), Accumulated Amortization 288,828 270,272  
Intangible assets with finite lives (amortized), Net Book Value $ 67,103 87,314  
Weighted average useful lives (in years) 10 years    
Trademarks And Trade Names [Member]      
Intangible assets with finite lives (amortized), Gross Carrying Amount $ 18,891 19,054  
Intangible assets with finite lives (amortized), Accumulated Amortization 15,260 14,786  
Intangible assets with finite lives (amortized), Net Book Value $ 3,631 4,268  
Weighted average useful lives (in years) 11 years    
Other [Member]      
Intangible assets with finite lives (amortized), Gross Carrying Amount $ 3,910 4,003  
Intangible assets with finite lives (amortized), Accumulated Amortization 3,910 4,003  
Intangible assets with finite lives (amortized), Net Book Value $ 0 $ 0