## On Some Series Related to Möbius Function and Lambert W-Function

**Authors:** Danil Krotkov

We derive some new formulas, connecting some series with Möbius function with Sine Integral and Cosine Integral functions, give the formal proof for full version of Stirling's formula with remainder term in form of definite integral of elementary function; investigate the values of new Dirichlet series function at natural numbers >1 and its behavior at the pole at s=1, connecting it with elementary constants.

**Comments:** 13 Pages.

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### Submission history

[v1] 2016-04-15 04:23:52

[v2] 2016-06-12 04:36:26

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