Summing Lambert Series in Euler's q-Exponential Functions

2018/11/16 by Ruiming Zhang, Zhang, Ruiming
Engineering · Physics and Astronomy · Decision Sciences · #Sports Dynamics and Biomechanics #Experimental and Theoretical Physics Studies #Multidisciplinary Science and Engineering Research

paper · pdf · doi:10.48550/arxiv.1811.07756

Abstract

In the work we shall present formulas to sum Lambert series using Euler's q-exponential functions, and several Lambert series associated with well-known arithmetic functions are given as examples. These functions are: the Möbius μ(n), the Euler's totient φ(n), Jordan's totient J_k(n), von Mangoldt Λ(n), divisor function σ_s(n), the Ramanujan's sum c_q(n) , and sum of square functions r₂(n),r₄(n),r₈(n).

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