$\int_0^\infty e^{i \pi x} \left(1-(x+1)^{\frac{1}{x+1}}\right) dx$

Posted 8 months ago
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$\int_0^\infty e^{i \pi x} \left(1-(x+1)^{\frac{1}{x+1}}\right) dx$

To be continued. Answer
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Posted 8 months ago Answer
Posted 8 months ago
 I won't bring the subject of numerical computation into this discussion, but I spent several years learning to compute the digits of $\int_0^\infty{e^{i \pi x} \left(1-(x+1)^{\frac{1}{x+1}}\right)}dx.$ You can read about my adventure at How to calculate the digits of the MKB constant. If you like numeric computations, of much interest is the story of how I came across this integral, by investigating $\sum _{x=0}^{\infty } e^{i \pi x} \left(1-(x+1)^{\frac{1}{x+1}}\right)$ since the 1990s, at Try to beat these MRB constant records! Answer
Posted 7 months ago
 So, I could conclude that The following "proof of it is from combining andWhile   Something similar is shown:        That looks like it proves to me. But I don't see any proof for . Answer
Posted 7 months ago Answer
Posted 5 months ago Answer
Posted 3 months ago
 MRB=$\sum _{x=0}^{\infty } e^{i \pi x} \left(1-(x+1)^{\frac{1}{x+1}}\right)$ vs M2= $\int_0^\infty e^{i \pi x} \left(1-(x+1)^{\frac{1}{x+1}}\right) dx$ in proper integrals See this notebook. I got an interesting co-answer here.  Answer