Pentti Haukkanen

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 4, Pages 44-57

DOI: 10.7546/nntdm.2019.25.4.44-57

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## Details

### Authors and affiliations

Pentti Haukkanen

*Faculty of Information Technology and Communication Sciences
FI-33014 Tampere University, Finland
*

### Abstract

We present the theory of formal power series in several variables in an elementary way. This is a generalization of Niven’s theory of formal power series* *in one variable. We refer to a formal power series in *n* variables as an *n*-way array of complex or real numbers and investigate its algebraic properties without analytic tools. We also consider the formal derivative, logarithm and exponential of a formal power series in *n* variables. Applications to multiplicative arithmetical functions in several variables and cumulants in statistics are presented.

### Keywords

- Formal power series
- Derivative
- Logarithm
- Exponential function
- Arithmetical functions in several variables
- Cumulants

### 2010 Mathematics Subject Classification

- 13F25
- 11A25
- 62E10

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## Cite this paper

Haukkanen, P. (2019). Formal power series in several variables. Notes on Number Theory and Discrete Mathematics, 25(4), 44-57, doi: 10.7546/nntdm.2019.25.4.44-57.