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Revenue from Contracts with Customers - Additional Information (Details) - USD ($)
 12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Revenue from External Customer [Line Items]    
Contract with customer, asset, expected to be transferred to receivables within the next 12 months and therefore $ 8,200,000  
Contract with customer other current asset   $ 6,900,000
Contract with customer other long-term assets   5,000,000.0
Contract with customer, asset, reclassified to receivable 6,600,000  
Contract with customer, asset, increase in contract assets (900,000)  
Contract with customer, asset, increase in contract assets related to revenue recognized 7,500,000  
Deferred revenue, revenue recognized 402,500,000  
Deferred revenue, additions 458,200,000  
Short term and long term accounts receivable $ 744,600,000 511,300,000
Capitalized contract cost, amortization period 5 years  
Amortization expense related to costs to obtain a contract with a customer $ 46,700,000 36,200,000
Impairments of the contract cost asset 0 0
Deferred revenue 497,677,000 426,465,000
Revenue, remaining performance obligation, amount 1,485,000,000.0  
Unrecorded    
Revenue from External Customer [Line Items]    
Revenue, remaining performance obligation, amount 987,300,000  
Other Current Assets    
Revenue from External Customer [Line Items]    
Capitalized contract cost, net 40,200,000 33,900,000
Other Assets    
Revenue from External Customer [Line Items]    
Capitalized contract cost, net 81,100,000 $ 72,900,000
Arena Solutions    
Revenue from External Customer [Line Items]    
Deferred revenue increased 15,500,000  
Deferred revenue fair value adjustment net $ 10,400,000