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Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Dec. 31, 2020 | Sep. 30, 2020
--- | --- | ---
Goodwill (not amortized) | $ 1,635,281 | $ 1,625,786
Intangible assets with finite lives (amortized), Gross Carrying Amount | 919,868 | 911,809
Intangible assets with finite lives (amortized), Accumulated Amortization | 693,972 | 674,239
Intangible assets with finite lives (amortized), Net Book Value | 225,896 | 237,570
Intangible Assets, Net (Including Goodwill) | 1,861,177 | 1,863,356
Purchased Software |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 446,336 | 443,275
Intangible assets with finite lives (amortized), Accumulated Amortization | 317,753 | 309,124
Intangible assets with finite lives (amortized), Net Book Value | 128,583 | 134,151
Capitalized Software |  |
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 and Relationships |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 423,719 | 418,953
Intangible assets with finite lives (amortized), Accumulated Amortization | 332,787 | 322,092
Intangible assets with finite lives (amortized), Net Book Value | 90,932 | 96,861
Trademarks and Trade Names |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 22,854 | 22,687
Intangible assets with finite lives (amortized), Accumulated Amortization | 16,473 | 16,129
Intangible assets with finite lives (amortized), Net Book Value | 6,381 | 6,558
Other |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 4,082 | 4,017
Intangible assets with finite lives (amortized), Accumulated Amortization | 4,082 | 4,017
Intangible assets with finite lives (amortized), Net Book Value | $ 0 | $ 0

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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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