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Summary of Significant Accounting Policies - Hedging Activities (Details)
$ in Thousands, € in Millions
12 Months Ended
Sep. 30, 2022
USD ($)
Sep. 30, 2021
USD ($)
Sep. 30, 2020
USD ($)
Sep. 30, 2022
EUR (€)
Feb. 23, 2022
USD ($)
Feb. 01, 2022
USD ($)
Feb. 01, 2022
EUR (€)
Derivative [Line Items]              
Unrealized gain on derivative asset, net of tax effects $ 93,020            
Interest income 20,286 $ 632 $ 849        
Foreign Exchange Contract [Member] | Designated as Hedging Instrument              
Derivative [Line Items]              
Unrealized gain on derivative asset, net of tax effects 93,000            
Currency Swap | Designated as Hedging Instrument              
Derivative [Line Items]              
Derivative, notional amount, cross-currency swap, exchanged           $ 1,030,000  
Derivative, notional amount, cross-currency swap, received | €             € 915
Derivative, notional amount           $ 960,000  
Derivative, fixed interest rate (as a percent)           1.283% 1.283%
Derivative, notional amount, cross-currency swap, maturity, deliver | €       € 852      
Derivative, notional amount, cross-currency swap, maturity, receive         $ 960,000    
Derivative, forward exchange rate         1.1261    
Gain to accumulated other comprehensive income 124,800            
Unrealized gain on derivative asset, net of tax effects 93,000            
Interest income $ 8,200            
Currency Swap | Designated as Hedging Instrument | Weighted Average              
Derivative [Line Items]              
Derivative, variable interest rate           1.196% 1.196%