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ζ-Function method for infinite series

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Abstract

The ζ-function method is used to rearrange Dirichlet series of the form

$$\sum\nolimits_m {( \pm )^m m^{ - s} g(x/m)}$$

into power series in x. This displays explicitly the analyticity in s of the series. Generalized ζ-functions of physical interest can be analysed by this method.

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References

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Authors and Affiliations

  1. Department of Physics, The Pennsylvania State University, 18051, Fogelsville, PA, USA

    Alfred Actor

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  1. Alfred Actor
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Actor, A. ζ-Function method for infinite series. Letters in Mathematical Physics 12, 357–362 (1986). https://doi.org/10.1007/BF00402669

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  • DOI: https://doi.org/10.1007/BF00402669

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