the catalan identites are interesting, and it is likely that most of them are true. however, the so-called "proofs" (i.e., mathematica output) are not really proofs. even the current version of mathematica has bugs. for example, version 6.0.2 says this series does not converge: Sum[((-1)^(n + 1) + Cos[n Pi/2])/n, {n, 1, Infinity}] even though the sum is Log[2]/2, and even though the two previous versions of mathematica gave the correct answer. the bottom line is, don't accept output unless you can verify it through an independent calculation. bob baillie --- rwg@sdf.lonestar.org wrote:
from http://www.cs.cmu.edu/~adamchik/articles/catalan/catalan.htm In[1]:=Integrate[ArcSin[Sinh[t]], {t, 0, ArcSinh[1]}]
Out[1]=-Catalan + (1/4)*Pi*Log[3 + 2*Sqrt[2]]
(Not the trivial changevar of the ArcSinh[Sin[]].)
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