4 problems

For positive integers $r$ and $s$, define the generalized Apéry polynomials by … A polynomial sequence $(f_n(q))_{n\ge 0}$ is $q$-log-convex when the coefficients of…

Let $n$ be a positive integer, let $m\in\{1,2,3,\ldots\}$, let $x$ be an indeterminate, and let … be the Apéry polynomial. For $\epsilon\in\{1,-1\}$, Sun's conjecture. … This predi…

Let $p$ be an odd prime, let $A_k(x)$ denote the Apéry polynomials used in the source, and define $c(p)$ by the congruence in (1.9). The source's congruences (1.9) and (1.10) give…

Let $A_k=A_k(1)$ denote the Apéry numbers, where … Let $p$ be an odd prime. Sun's conjecture. … This is one of Z.-W. Sun's conjectures on congruences for sums of Apéry polynomials;…