Goodwill and Intangible Assets - Amortization Expense (Details) - USD ($) $ in Millions	12 Months Ended
Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization of intangible assets	$ 41.8	$ 35.2	$ 24.2

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
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3602-108585

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
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-URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
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-Section 45
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-URI http://asc.fasb.org/extlink&oid=6388964&loc=d3e16225-109274

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