The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-SubTopic 10
-Topic 230
-Publisher FASB
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-Name Accounting Standards Codification
-Topic 350
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Goodwill and Other Intangible Assets - Additional Information (Details) - USD ($)	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Goodwill and Other Intangible Assets
Amortization expense related to intangible assets	$ 28,953,000	$ 25,936,000	$ 20,829,000
Finite-Lived Intangible Asset, Expected Amortization, Year One	17,000,000
Finite-Lived Intangible Asset, Expected Amortization, Year Two	14,500,000
Asset Impairment Charges	0
Fair value of financial instruments	$ 0
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