60 citations · 677 across the 102 of their papers we have counts for
11 papers · 1 filter
A fast approximation to supershell partition functions
Bran G. Wilson, Jean-Christophe Pain
A formula for supershell partition functions, which play a major role in the Super Transition Array approach to radiative-opacity calculations, is derived as a functional of the di…
A summation formula for generalized -bonacci numbers
Jean-Christophe Pain
In this note, we present a simple summation formula for -bonacci numbers. The derivation consists in obtaining the generating function of such numbers, and noting that its evalu…
From Fourier series to infinite product representations of and infinite-series forms for its positive powers
Jean-Christophe Pain
In this article, we derive, using Fourier series and multiple derivative of the function , series representations for positive powers of . We also show that the Eule…
New series representations for any positive power of from a relation involving trigonometric functions
Jean-Christophe Pain
In previous works, we presented series representations for and , in which the prefactor depends only on the golden ratio appears. In this article, we derive a general re…
Series representations for involving the golden ratio
Jean-Christophe Pain
Although many series exist for and , very few are known for . In this article, we derive, using a trigonometric identity obtained by Euler, two representations of $π^…
Relations between and the golden ratio in the form of Bailey-Borwein-Plouffe-type formulas
Jean-Christophe Pain
We provide a family of expressions of in terms of the golden ratio in the same spirit of the formula obtained by Bailey, Borwein and Plouffe for . Connection with cyclot…