Goodwill and Intangible Assets (Goodwill and Acquired Intangible Assets) (Details) - USD ($) $ in Thousands	Mar. 28, 2020	Sep. 30, 2019
Goodwill (not amortized)	$ 1,603,081	$ 1,238,179
Intangible assets with finite lives (amortized), Gross Carrying Amount	889,489	778,968
Intangible assets with finite lives (amortized), Accumulated Amortization	638,298	609,019
Intangible assets with finite lives (amortized), Net Book Value	251,191	169,949
Intangible Assets, Net (Including Goodwill)	1,854,272	1,408,128
Purchased software
Intangible assets with finite lives (amortized), Gross Carrying Amount	427,092	377,359
Intangible assets with finite lives (amortized), Accumulated Amortization	292,756	278,144
Intangible assets with finite lives (amortized), Net Book Value	134,336	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	413,054	355,931
Intangible assets with finite lives (amortized), Accumulated Amortization	303,095	288,828
Intangible assets with finite lives (amortized), Net Book Value	109,959	67,103
Trademarks and trade names
Intangible assets with finite lives (amortized), Gross Carrying Amount	22,524	18,891
Intangible assets with finite lives (amortized), Accumulated Amortization	15,628	15,260
Intangible assets with finite lives (amortized), Net Book Value	6,896	3,631
Other
Intangible assets with finite lives (amortized), Gross Carrying Amount	3,942	3,910
Intangible assets with finite lives (amortized), Accumulated Amortization	3,942	3,910
Intangible assets with finite lives (amortized), Net Book Value	$ 0	$ 0