Business Segment Information - Schedule of Segment Revenue (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Segment Reporting Information [Line Items]
Revenue	$ 293,958,599	$ 262,173,411	$ 238,587,006
Operating segments | U.S. Healthcare Solutions
Segment Reporting Information [Line Items]
Revenue	265,339,427	234,759,218	212,100,202
Operating segments | U.S. Healthcare Solutions | Human Health
Segment Reporting Information [Line Items]
Revenue	259,973,909	229,716,669	207,284,444
Operating segments | U.S. Healthcare Solutions | Animal Health
Segment Reporting Information [Line Items]
Revenue	5,365,518	5,042,549	4,815,758
Operating segments | International Healthcare Solutions
Segment Reporting Information [Line Items]
Revenue	28,627,542	27,418,679	26,491,673
Operating segments | International Healthcare Solutions | Alliance Healthcare
Segment Reporting Information [Line Items]
Revenue	23,061,721	22,349,278	21,890,402
Operating segments | International Healthcare Solutions | Other Healthcare Solutions
Segment Reporting Information [Line Items]
Revenue	5,565,821	5,069,401	4,601,271
Intersegment eliminations
Segment Reporting Information [Line Items]
Revenue	$ (8,370)	$ (4,486)	$ (4,869)