Business Acquisitions Business Acquisitions - Prior Year (Details) - USD ($)	12 Months Ended
	Sep. 30, 2019	Sep. 30, 2018
Business Acquisition [Line Items]
Contingent and deferred acquisition payments	$ 17,470,000	$ 14,211,000
Number of Years in Measurement Period from Acquisition Date to Change Underlying Assumptions	6 years	5 years 10 months 24 days
Other Acquisitions [Member]
Business Acquisition [Line Items]
Payments to Acquire Businesses, Gross	$ 129,500,000	$ 97,400,000
Issuance of common stock in connection with business and asset acquisitions (in shares)		844,108
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net	62,900,000	$ 62,300,000
Identifiable Intangible Assets Acquired	60,800,000	39,100,000
Cash and Cash Equivalents [Member] | Other Acquisitions [Member]
Business Acquisition [Line Items]
Payments to Acquire Businesses, Gross	114,600,000	75,700,000
Share Distribution [Member] | Other Acquisitions [Member]
Business Acquisition [Line Items]
Payments to Acquire Businesses, Gross	13,400,000
Contingent Consideration Payments [Member] | Other Acquisitions [Member]
Business Acquisition [Line Items]
Payments to Acquire Businesses, Gross	$ 2,000,000.0	$ 8,300,000