Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Thousands	Sep. 30, 2020	Sep. 30, 2019
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangibles, accumulated amortization	$ (681,487)	$ (593,221)
Total other intangible assets, gross carrying amount	2,567,594	2,888,057
Total other intangible assets, net carrying amount	1,886,107	2,294,836
Trade names
Indefinite-lived Intangible Assets [Line Items]
Indefinite-lived intangibles	$ 685,312	685,324
Customer relationships
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible asset, weighted average remaining useful life	13 years
Finite-lived intangibles, gross carrying amount	$ 1,671,888	1,931,212
Finite-lived intangibles, accumulated amortization	(565,372)	(489,471)
Finite-lived intangibles, net carrying amount	$ 1,106,516	1,441,741
Trade names and other
Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible asset, weighted average remaining useful life	14 years
Finite-lived intangibles, gross carrying amount	$ 210,394	271,521
Finite-lived intangibles, accumulated amortization	(116,115)	(103,750)
Finite-lived intangibles, net carrying amount	$ 94,279	$ 167,771