Equity-based Compensation - Employee Equity-Based Compensation Pre-Tax Expense (Detail) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items]
Equity-based compensation pre-tax expense	$ 104,540	$ 89,698	$ 71,807
Cost of Revenue [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items]
Equity-based compensation pre-tax expense	53,409	42,969	32,096
Research and Development [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items]
Equity-based compensation pre-tax expense	8,644	7,509	5,631
Selling, General and Administrative [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items]
Equity-based compensation pre-tax expense	$ 42,487	$ 39,220	$ 34,080