Notes on Number Theory and Discrete Mathematics
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Volume 25, 2019, Number 4, Pages 44-57
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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.
- Formal power series
- Exponential function
- Arithmetical functions in several variables
2010 Mathematics Subject Classification
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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.