This time we will compute the Imaginary part first to at least 500 digits: a = 0 For, 50 n] Print - a], Until further notice in this post when we compute the imaginary part of M1, we will be concerned with the imaginary part's absolute value only, We can compute plenty of digits of the integral analog of the MRB constant' (I once called it the MKB constant, named after Marsha Kell-Burns my, now ex, wife.) In the paper, Mathar simply calls it M1. Going back to integral analog of the MRB constant' Notice that WorkingPrecision->100 gave 51 consistent (correct) digits, WorkingPrecision->120 gave 62 correct digits, WorkingPrecision->150 gave 76 correct digits, WorkingPrecision->200 gave 102 correct digits, so it is not too much of a stretch to believe WorkingPrecision->250 gave 125 correct digits. However, they are not proven to be correct yet!
I've gotten Mathematica to compute 125 digits.
M1 (MKB) can be written as and integral of a power of e: Richard Mathar did a lot of work on it here, where M is the MRB constant and M1 is MKB: What about records of computing the integral analog of the MRB constant? (I call it the MKB constant.) See Google Scholar MKB constant.
Is anyone interested in improving or disproving this conjecture? It appears that the absolute value, minus 1/2, of the limit(integral of (-1)^x x^(1/x) from 1 to 2N as N->infinity) would equal the partial sum of (-1)^xx^(1/x) from 1 to where the upper summation is even and growing without bound.
Wolfram Data Framework Semantic framework for real-world data.
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