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Goodwill and Other Intangible Assets - Additional Information (Details) - USD ($)
12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Goodwill and Other Intangible Assets      
Amortization expense related to intangible assets $ 32,804,000 $ 28,953,000 $ 25,936,000
Asset Impairment Charges 0    
Fair value of financial instruments 0    
Maximum      
Goodwill and Other Intangible Assets      
Intangible asset amortization fiscal year from 2025 to 2029 33,000,000    
Minimum      
Goodwill and Other Intangible Assets      
Intangible asset amortization fiscal year from 2025 to 2029 $ 31,000,000    
Customer Relationships | Maximum      
Goodwill and Other Intangible Assets      
Expected remaining useful life 20 years    
Customer Relationships | Minimum      
Goodwill and Other Intangible Assets      
Expected remaining useful life 13 years    
Patents | Maximum      
Goodwill and Other Intangible Assets      
Expected remaining useful life 20 years    
Patents | Minimum      
Goodwill and Other Intangible Assets      
Expected remaining useful life 10 years    
Capitalized software | Maximum      
Goodwill and Other Intangible Assets      
Expected remaining useful life 7 years    
Capitalized software | Minimum      
Goodwill and Other Intangible Assets      
Expected remaining useful life 3 years