Various conjectural series identities
read the original abstract
In this paper we collect over 150 new series identities (involving binomial coefficients) conjectured by the author in 2026. The values involved are related to $\pi$ or Riemann's zeta function or Dirichlet's $L$-function. For example, we conjecture that $$\sum_{k=0}^\infty\frac{16k+3}{(-202^2)^k}\binom{2k}kT_k(19,-20)T_{2k}(9,-5)=\frac{43\sqrt{101}}{75\pi},$$ where $T_n(b,c)$ denotes the coefficient of $x^n$ in the expansion of $(x^2+bx+c)^n$. The conjectures in this paper might interest some readers and stimulate further research.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
Evaluations of some series via the WZ method
The authors prove via the WZ method that a quintuple central binomial sum equals 3/π and that the sum of a fourth derivative of a gamma ratio equals 1959/2 ζ(6) minus 432 ζ(3)^2.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.