Goodwill and Intangibles - Schedule of Acquired Intangibles in Accompanying Consolidated Balance Sheets (Details) $ in Thousands	12 Months Ended
Sep. 30, 2022 USD ($)
Finite-lived Intangible Assets [Roll Forward]
Beginning balance	$ 1,565,758
Acquired	163,919
Amortization	(198,602)
Foreign currency translation and other	(137,023)
Ending balance	$ 1,394,052
Weighted Average Amortization Period (years)	9 years
Customer Relationships, Contracts and Backlog
Finite-lived Intangible Assets [Roll Forward]
Beginning balance	$ 1,309,061
Acquired	101,527
Amortization	(175,592)
Foreign currency translation and other	(98,558)
Ending balance	$ 1,136,438
Weighted Average Amortization Period (years)	7 years
Developed Technology
Finite-lived Intangible Assets [Roll Forward]
Beginning balance	$ 40,020
Acquired	62,000
Amortization	(12,055)
Foreign currency translation and other	(1,034)
Ending balance	$ 88,931
Weighted Average Amortization Period (years)	7 years
Trade Names
Finite-lived Intangible Assets [Roll Forward]
Beginning balance	$ 216,677
Acquired	392
Amortization	(10,955)
Foreign currency translation and other	(37,431)
Ending balance	$ 168,683
Weighted Average Amortization Period (years)	18 years

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.

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Amount of foreign currency translation gain (loss) which increases (decreases) assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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Amount after amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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Remaining amortization period of finite-lived intangible assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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Amount of increase in assets, excluding financial assets, lacking physical substance with a definite life, from an acquisition.

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