Monday Math 35

In a previous post, we found that . What, then, is ?

Previously, we found that for , . Similarly, as , we see that with , . Setting , we see , for .

Thus
.

As we did previously, we solve the integral in each term with the substitution , which gives us:
.

Plugging into our series,
.

We should recognize that last sum as the Dirichlet eta function. Thus, just as , we see .

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One Response to “Monday Math 35”

  1. Monday Math 55 « Twisted One 151’s Weblog Says:

    […] . Reversing the order of the double integration, and performing the inner integral, We found previously that , so then (for ) and, in analogy to I(s), we can also find that. Possibly related posts: […]

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