I can't seem to find an answer as to why there are two conventions for Bernoulli numbers. I have done a fair amount of research and can't find a definitive answer. Maybe I am just not reading between the lines but I would greatly appreciate any insight on the topic.
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Because there are two definitions of the Bernoulli Numbers. Do you mean that there are two conventions for Bernoulli polynomials? i.e. $B_n(x)$ or $B_n^*(x)$. – Mr Pie Feb 16 '18 at 00:10
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Go here $\longrightarrow$ http://mathworld.wolfram.com/BernoulliNumber.html to know how to distinguish each of the definitions $B_n$ and $B_n^$. I must say though, it ia weird because for polynomials, $B_n(x) = B_n^(x)$. – Mr Pie Feb 16 '18 at 00:17