We obtain an explicit formula in terms of the partitions of the positive integer n to express the nth coefficient of the formal series expansion of the reciprocal of a given function. A brief survey shows that our arithmetic proof differs from others, some obtained already in the XIX century. Examples are given to establish explicit formulas for Bernoulli, Euler, and Fibonacci numbers.

Reciprocal Function Series Coefficients with Integer Partitions

Talamini, Vittorino
2018-01-01

Abstract

We obtain an explicit formula in terms of the partitions of the positive integer n to express the nth coefficient of the formal series expansion of the reciprocal of a given function. A brief survey shows that our arithmetic proof differs from others, some obtained already in the XIX century. Examples are given to establish explicit formulas for Bernoulli, Euler, and Fibonacci numbers.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1123515
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