I have responded << Viewed on an iMac with Safari browser under OS 10.8.4 , eight of these line drawings display as unreadable thumbnail size; from "The real Bernoulli function" to "Euler's summation formula, as written by Euler" . At a quick glance you make very detailed and coherent argument. I have considerable sympathy, having recently expended much effort in documenting a similarly entrenched dichotomy regarding the definition of binomial coefficients --- wherein it is noteworthy that both Mathematica and Maple find themselves again on the wrong side of the fence --- see https://www.dropbox.com/s/anykne0pd55ehjg/binomial.pdf I hope you will not remain so offended by Knuth's response to your initial post, which was frankly far less convincing. These questions are genuinely difficult to resolve; and no professional is going to casually discard his entrenched conventions without a good deal of persuasion. WFL >> On 9/15/13, Hans Havermann <gladhobo@teksavvy.com> wrote:
Back in 2004, Peter Luschny wrote an open letter to Donald E. Knuth about his conviction that the proper definition of the Bernoulli number B(1) should be 1/2, not -1/2. Professor Knuth declined to embrace the idea.
http://www.luschny.de/math/zeta/OpenLetter.pdf
Peter has now put up a detailed response to Knuth, calling it The Bernoulli Manifesto.
http://luschny.de/math/zeta/The-Bernoulli-Manifesto.html
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