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May 28, 2010 at 17:03 comment added Pietro Majer "Legendre's reasons...are obscure". The main issue in my opinion is slightly different. Let's recall that 200 years ago (but even more recently) standardizing the notation was much more a difficult problem, and less urgent at the same time -no internet, no common scientific language, no or very few international meetings. In such a situation it was quite natural and harmless even introducing a notation ad hoc in any new memoir. Note that Weierstrass' one was the "factorial function", Fc(z), the reciprocal of the Gamma function.
Apr 10, 2010 at 23:28 vote accept Kevin Casto
Apr 10, 2010 at 23:27 comment added Kevin Casto Yeah, this is basically what I assumed. It is nice to have someone directly address the issue instead of sweeping it under the rug. And for those interested, the book is on Google Books - books.google.com/books?id=5uLAoued_dIC - and pages 8-10 have most of the identities listed above.
Apr 10, 2010 at 22:45 history answered Will Jagy CC BY-SA 2.5