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Goodwill and Acquired Intangible Assets (Goodwill and Acquired Intangible Assets) (Details) - USD ($) $ in Thousands | 12 Months Ended |  |
--- | --- | --- | ---
Sep. 30, 2019 | Sep. 30, 2018 | Sep. 30, 2017
Goodwill (not amortized), Net Book Value | $ 1,238,179 | $ 1,182,457 | $ 1,182,772
Intangible assets with finite lives (amortized), Gross Carrying Amount | 778,968 | 766,199 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 609,019 | 565,997 |
Intangible assets with finite lives (amortized), Net Book Value | 169,949 | 200,202 |
Intangible Assets, Net (Including Goodwill) | 1,408,128 | 1,382,659 |
Purchased Software [Member] |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 377,359 | 362,679 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 278,144 | 254,059 |
Intangible assets with finite lives (amortized), Net Book Value | $ 99,215 | 108,620 |
Weighted average useful lives (in years) | 9 years |  |
Capitalized Software [Member] |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | $ 22,877 | 22,877 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 22,877 | 22,877 |
Intangible assets with finite lives (amortized), Net Book Value | 0 | 0 |
Customer Lists [Member] |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 355,931 | 357,586 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 288,828 | 270,272 |
Intangible assets with finite lives (amortized), Net Book Value | $ 67,103 | 87,314 |
Weighted average useful lives (in years) | 10 years |  |
Trademarks And Trade Names [Member] |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | $ 18,891 | 19,054 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 15,260 | 14,786 |
Intangible assets with finite lives (amortized), Net Book Value | $ 3,631 | 4,268 |
Weighted average useful lives (in years) | 11 years |  |
Other [Member] |  |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | $ 3,910 | 4,003 |
Intangible assets with finite lives (amortized), Accumulated Amortization | 3,910 | 4,003 |
Intangible assets with finite lives (amortized), Net Book Value | $ 0 | $ 0 |

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- Definition Weighted average amortization period of finite-lived intangible assets acquired either individually or as part of a group of assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 1 -Subparagraph (a)(3) -URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16265-109275 + Details
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- Definition Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 2 -Subparagraph (a)(1) -URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275 + Details
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- Definition Amount before amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 928 -SubTopic 340 -Section 50 -Paragraph 1 -URI http://asc.fasb.org/extlink&oid=6473545&loc=d3e61844-108004 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 2 -Subparagraph (a)(1) -URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275 + Details
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- Definition Carrying amount of finite-lived intangible assets, indefinite-lived intangible assets and goodwill. Goodwill is an asset representing the future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized. Intangible assets are assets, not including financial assets, lacking physical substance. + References No definition available. + Details
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