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MRB constant S

January 02 2012 by Marvin Ray Burns 465
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Let f(c)= sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity)

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Then f(1) = the MRB constant:

evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 1)) = .1878596425NULL

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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)) = -1.351776595 

evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 7.020400867228059)) = 7.020400867

evalf(eval(sum((-1)^n*(n^(c/n)-c), n = 1 .. infinity), c = 25.58774196597964)) = 25.58880851

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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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Download jan022012.mw

 

 

 

 

marvinrayburns.com
constants

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