Goodwill and Other Intangible Assets - Components of Other Intangible Assets (Details) - USD ($) $ in Thousands	Sep. 30, 2021	Sep. 30, 2020
Other intangible assets subject to amortization:
Gross Carrying Amount	$ 857,867	$ 821,772
Accumulated Amortization	279,603	197,978
Net	578,264	623,794
Other intangible assets not subject to amortization:
Other intangible assets not subject to amortization	47,170	47,170
Total other intangible assets, gross	905,037	868,942
Total other intangible assets, net	625,434	670,964
Other indefinite-lived intangibles
Other intangible assets not subject to amortization:
Other intangible assets not subject to amortization	47,170	47,170
Customer relationships, trade names, and distribution rights
Other intangible assets subject to amortization:
Gross Carrying Amount	701,849	690,716
Accumulated Amortization	207,606	140,037
Net	494,243	550,679
Product technology, trade secrets and know-how
Other intangible assets subject to amortization:
Gross Carrying Amount	147,270	122,135
Accumulated Amortization	63,249	49,228
Net	84,021	72,907
Acquired patents and licenses
Other intangible assets subject to amortization:
Gross Carrying Amount	8,748	8,921
Accumulated Amortization	8,748	8,713
Net	$ 0	$ 208