Jesús Guillera

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math.NT2025

Fast formulas for the Hurwitz values $I^¶ (2, a)$ and $I^¶ (3, a)$

JesÃºs Guillera

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

math.NT2025

The fastest series for $1/ I ¨ $ due to Ramanujan. Proofs from modular polynomials

JesÃºs Guillera

First we give general formulas for proving real or complex Ramanujan series for $1/ I ¨ $ . Then, as an example, we apply them for providing complete proofs of the fastest series for $…

math.NT2025

The WZ method and flawless WZ pairs

JesÃºs 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.NT2024

Heuristic derivation of Zudilin's supercongruences for rational Ramanujan series

JesÃºs 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.

Fast formulas for the Hurwitz values I^¶(2,a) and I^¶(3,a)

The fastest series for 1/I¨ due to Ramanujan. Proofs from modular polynomials

The WZ method and flawless WZ pairs

Heuristic derivation of Zudilin's supercongruences for rational Ramanujan series

Fast formulas for the Hurwitz values $I^¶ (2, a)$ and $I^¶ (3, a)$

The fastest series for $1/ I ¨ $ due to Ramanujan. Proofs from modular polynomials