Jesús Guillera

activity

20052025

most citedDouble integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent

92 citations · 228 across the 39 of their papers we have counts for

collaborators

41 papers

math.NT2025

Fast formulas for the Hurwitz values $ζ (2, a)$ and $ζ (3, a)$

Jesús Guillera

We prove two fast formulas for the Hurwitz values $ζ (2, a)$ and $ζ (3, a)$ respectively with the help of the WZ method. In them $(a)_{n}$ denotes the rising factorial or Pochhammer's sy…

math.NT2025

The WZ method and flawless WZ pairs

Jesús Guillera

Recently, Kam Cheong Au discovered a powerful methodology of finding new Wilf-Zeilberger (WZ) pairs. He calls it WZ seeds and gives numerous examples of applications to proving lon…

math.NT2023

Heuristic derivation of Zudilin's supercongruences for rational Ramanujan series

Jesús Guillera

We derive, using a heuristic method, a $p$ -adic mate of bilateral Ramanujan series. It has (among other consequences) the Zudiln's supercongruences for rational Ramanujan series.

math.NT2021★ 1 cited

Rational Hypergeometric Ramanujan Identities for $1/ π^{c}$ : Survey and Generalizations

Henri Cohen, Jesús Guillera

We give a simple unified proof for all existing rational hypergeometric Ramanujan identities for $1/ π$ , and give a complete survey (without proof) of several generalizations: ratio…

math.NT2020

Proof of Chudnovskys' series for $1/ π$

Jesús Guillera

We prove rational alternating Ramanujan-type series of level $1$ discovered by the brothers David and Gregory Chudnovky, by using a method of the author. We have carried out the co…

math.NT2020

WZ proofs of Ramanujan-type series (via $_{2} F_{1}$ evaluations)

Jesús Guillera

We use Zeilberger's algorithm for proving some identities of Ramanujan-type via $_{2} F_{1}$ evaluations.

Fast formulas for the Hurwitz values ζ(2,a) and ζ(3,a)

The WZ method and flawless WZ pairs

Heuristic derivation of Zudilin's supercongruences for rational Ramanujan series

Rational Hypergeometric Ramanujan Identities for 1/πc: Survey and Generalizations

Proof of Chudnovskys' series for 1/π

WZ proofs of Ramanujan-type series (via 2​F1​ evaluations)

Fast formulas for the Hurwitz values $ζ (2, a)$ and $ζ (3, a)$

Rational Hypergeometric Ramanujan Identities for $1/ π^{c}$ : Survey and Generalizations

Proof of Chudnovskys' series for $1/ π$

WZ proofs of Ramanujan-type series (via $_{2} F_{1}$ evaluations)