MRB constant S

Posted: Marvin Ray Burns 550 Product: Maple

January 02 2012

Let f(c)= sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity)

Then f(1) = the MRB constant:

evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 1)) =

What if we change the value of c and use Levin's u-transform to compute the values for the analytic extension of the sum?

Then can we find values for c such that f(c)=c?

evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = -1.351776595077954)) =

evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 7.020400867228059)) =

evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 25.58774196597964)) =

As an alalytic extension of the sum is there another value for c such that f(c) = the MRB constant? I haven't found one.

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