Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Jun. 27, 2020	Sep. 30, 2019
Goodwill (not amortized)	$ 1,605,204	$ 1,238,179
Intangible assets with finite lives (amortized), Gross Carrying Amount	900,895	778,968
Intangible assets with finite lives (amortized), Accumulated Amortization	653,722	609,019
Intangible assets with finite lives (amortized), Net Book Value	247,173	169,949
Intangible Assets, Net (Including Goodwill)	1,852,377	1,408,128
Purchased Software
Intangible assets with finite lives (amortized), Gross Carrying Amount	437,441	377,359
Intangible assets with finite lives (amortized), Accumulated Amortization	299,962	278,144
Intangible assets with finite lives (amortized), Net Book Value	137,479	99,215
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	414,084	355,931
Intangible assets with finite lives (amortized), Accumulated Amortization	311,117	288,828
Intangible assets with finite lives (amortized), Net Book Value	102,967	67,103
Trademarks and Trade Names
Intangible assets with finite lives (amortized), Gross Carrying Amount	22,541	18,891
Intangible assets with finite lives (amortized), Accumulated Amortization	15,814	15,260
Intangible assets with finite lives (amortized), Net Book Value	6,727	3,631
Other
Intangible assets with finite lives (amortized), Gross Carrying Amount	3,952	3,910
Intangible assets with finite lives (amortized), Accumulated Amortization	3,952	3,910
Intangible assets with finite lives (amortized), Net Book Value	$ 0	$ 0