- #1

Svein

Science Advisor

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## Main Question or Discussion Point

Continue reading...The goal is to get a little bit closer to the values of the zeta function (ζ(s)) and the eta function (η(s)) for some odd values of s. This insight is an expansion of two of my previous insights (Further Sums Found Through Fourier Series, Using the Fourier Series To Find Some Interesting Sums). You patience is appreciated as there are many equations to load on this page.

Specifically I will calculate the sums

[itex]\frac{1}{1^{p}}-\frac{1}{3^{p}} +\frac{1}{5^{p}}-\frac{1}{7^{p}}… [/itex]

[itex]\frac{1}{1^{p}}+\frac{1}{2^{p}}-\frac{1}{4^{p}} -\frac{1}{5^{p}}+\frac{1}{7^{p}}…[/itex]

[itex]\frac{1}{1^{p}}+\frac{1}{2^{p}}+\frac{1}{3^{p}}...