Goodwill and Other Intangible Assets - Components of Other Intangible Assets, Activity (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount, beginning balance	$ 821,772
Additions	37,200
Impairment	(3,175)
FX and Other	2,070
Gross carrying amount, ending balance	857,867
Accumulated Amortization	279,603	$ 197,978
Net	578,264	623,794
Indefinite-lived Intangible Assets [Line Items]
Other indefinite-lived intangibles, beginning balance	47,170
Other indefinite-lived intangibles, ending balance	47,170
Intangible Assets, Gross (Excluding Goodwill) [Abstract]
Total other intangible assets, gross	905,037	868,942
Finite-lived and indefinite-lived intangible assets acquired	37,200
Total other intangible assets, net	625,434	670,964
Other indefinite-lived intangibles
Indefinite-lived Intangible Assets [Line Items]
Other indefinite-lived intangibles, beginning balance	47,170
Other indefinite-lived intangibles, ending balance	47,170
Customer relationships, trade names, and distribution rights
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount, beginning balance	690,716
Additions	11,800
Impairment	(2,419)
FX and Other	1,752
Gross carrying amount, ending balance	701,849
Accumulated Amortization	207,606	140,037
Net	494,243	550,679
Product technology, trade secrets and know-how
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount, beginning balance	122,135
Additions	25,400
Impairment	(583)
FX and Other	318
Gross carrying amount, ending balance	147,270
Accumulated Amortization	63,249	49,228
Net	84,021	72,907
Acquired patents and licenses
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount, beginning balance	8,921
Additions	0
Impairment	(173)
FX and Other	0
Gross carrying amount, ending balance	8,748
Accumulated Amortization	8,748	8,713
Net	$ 0	$ 208