Condensed Consolidated Statements of Cash Flows (Unaudited) - USD ($)	6 Months Ended
	Mar. 31, 2020	Mar. 31, 2019
Operating Activities
Net Income (Loss) Attributable to Parent	$ 86,700,000	$ 91,700,000
Adjustments to reconcile net income to net cash, cash equivalents and restricted cash provided by operating activities:
Depreciation and Amortization of PP&E and Software	34,100,000	36,400,000
Acquisition-related intangible asset amortization	53,800,000	53,000,000.0
Amortization of Debt Issuance Costs and Discounts	2,100,000	3,200,000
Gain (Loss) on Extinguishment of Debt	15,600,000	0
Benefit for deferred income taxes	(8,400,000)	(8,200,000)
Loss (Gain) on disposal of property, equipment, intangible assets, and impairments	1,200,000	(200,000)
Stock compensation	19,000,000.0	16,900,000
Other Operating Activities, Cash Flow Statement	12,400,000	(4,100,000)
Change in working capital excluding cash, current debt, acquisitions and dispositions:
Trade accounts receivable	12,200,000	24,000,000.0
Inventories	(1,700,000)	(1,500,000)
Other current assets	(23,600,000)	3,700,000
Trade accounts payable	6,300,000	(6,600,000)
Accrued expenses and other liabilities	(55,200,000)	(54,300,000)
Increase (Decrease) in Accounts Receivable	(12,200,000)	(24,000,000.0)
Increase (Decrease) in Inventories	1,700,000	1,500,000
Increase (Decrease) in Other Operating Assets	23,600,000	(3,700,000)
Increase (Decrease) in Accounts Payable, Trade	6,300,000	(6,600,000)
Accrued expenses and other liabilities	(55,200,000)	(54,300,000)
Increase (Decrease) in Other Noncurrent Assets and Liabilities, Net	(2,200,000)	(4,200,000)
Net cash, cash equivalents and restricted cash provided by operating activities	156,700,000	158,200,000
Investing Activities
Purchases of property, plant, equipment and software	(46,100,000)	31,400,000
Proceeds on sale of property and equipment	1,400,000	3,100,000
Payments to Acquire Businesses, Gross	(13,100,000)	0
Payments to Acquire Intangible Assets	0	(17,100,000)
Payments to Acquire Investments	0	(26,600,000)
Other investing activities	(100,000)	(200,000)
Net cash, cash equivalents and restricted cash used in investing activities	(57,900,000)	(71,800,000)
Financing Activities
Payment of long-term debt	25,100,000	(100,000)
Borrowings on Revolving Credit Facility	190,000,000.0	(110,000,000.0)
Payments on Revolving Credit Facility	85,000,000.0	(105,000,000.0)
Borrowings on Securitization Facility	13,200,000	4,900,000
Payments on Securitization Facility	(17,700,000)	4,900,000
Principal Amount Outstanding on Loans Securitized or Asset-backed Financing Arrangement	32,600,000	37,500,000
Payments on Note Securitization Facility	(21,200,000)	28,400,000
Payment for Debt Extinguishment or Debt Prepayment Cost	(12,200,000)	0
Repayments of Senior Debt	(425,000,000.0)	0
Cash dividends	(28,700,000)	(27,400,000)
Proceeds on exercise of stock options	5,700,000	8,600,000
Payment, Tax Withholding, Share-based Payment Arrangement	(15,800,000)	(4,000,000.0)
Payments for Repurchase of Common Stock	(54,100,000)	75,000,000.0
Proceeds from (Payments for) Other Financing Activities	3,900,000	3,700,000
Net cash, cash equivalents and restricted cash used in financing activities	(439,400,000)	(80,100,000)
Effect of exchange rate changes on cash, cash equivalents and restricted cash	(2,700,000)	(2,300,000)
Net Cash Flows	(343,300,000)	4,000,000.0
Cash, Cash Equivalents and Restricted Cash:
Cash and cash equivalents	214,100,000	187,000,000.0
At beginning of period	214,100,000	183,000,000.0
At end of period	290,500,000	187,000,000.0
Capital Expenditures Incurred but Not yet Paid	4,000,000.0	300,000
Restricted Stock or Unit Expense	27,100,000	9,900,000
Equity Method Investment, Realized Gain (Loss) on Disposal	2,800,000
Treasury Stock, Value, Acquired, Cost Method	(54,100,000)	(75,000,000.0)
Net Income (Loss) Attributable to Parent	86,700,000	91,700,000
Treasury Stock [Member]
Financing Activities
Payment, Tax Withholding, Share-based Payment Arrangement	(15,800,000)	(4,000,000.0)
Cash, Cash Equivalents and Restricted Cash:
Treasury Stock, Value, Acquired, Cost Method	$ (54,100,000)	$ (75,000,000.0)