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MRB constant L

Posted: June 14 2010 by Marvin Ray Burns 465

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Product: Maple

The MRB constant is the upper limit point of the sequence of partial sums defined by s(n)= $sum((-1)^n*n^(1/n),n=1..infinity)$ .

Each summand is a real number. However, the function f(n)= $(-1)^n*n^(1/n)$ is a complex-valued function of a real number, n. This blog is a break in progression of the MRB constant series for the purpose of looking at the "complex" nature of this function. The function can be written in exponential form, $exp(I*n*Pi)*n^(1/n)$ .

With this first post I would like to demonstrate, in a Maple document, what happens to f [-2,0). When put together (-1,0) these graphs seem to be describing a hyperbolic spiral. I'm not sure if I'll have more to say, or not. As always, others are welcome to join in.