F. Ruiz

activity

19922023

most citedAsymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials

37 citations · 81 across the 6 of their papers we have counts for

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math.NT2023

The computation of $ζ (2 k)$ , $β (2 k + 1)$ and beyond by using telescoping series

Óscar Ciaurri, Luis M. Navas, Francisco J. Ruiz +1

We present some simple proofs of the well-known expressions for \[ ζ(2k) = \sum_{m=1}^\infty \frac{1}{m^{2k}}, \qquad β(2k+1) = \sum_{m=0}^\infty \frac{(-1)^m}{(2m+1)^{2k+1}}, \] w…

math.NT2012★ 16 cited

A simple computation of $ζ (2 k)$ by using Bernoulli polynomials and a telescoping series

Ó. Ciaurri, L. M. Navas, F. J. Ruiz +1

We present a new proof of Euler's formulas for $ζ (2 k)$ , where $k = 1, 2, 3, ...$ , which uses only the defining properties of the Bernoulli polynomials, obtaining the value of $ζ (2 k)$ …

math.NT2011★ 37 cited

Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials

Luis M. Navas, Francisco J. Ruiz, Juan L. Varona

We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials $B_{n} (x; λ)$ in detail. The starting point is their Fourier series on $[0, 1]$ which, it is shown,…

The computation of ζ(2k), β(2k+1) and beyond by using telescoping series

A simple computation of ζ(2k) by using Bernoulli polynomials and a telescoping series

Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials

The computation of $ζ (2 k)$ , $β (2 k + 1)$ and beyond by using telescoping series

A simple computation of $ζ (2 k)$ by using Bernoulli polynomials and a telescoping series