二级有限多重zeta值的加权和猜想的一个证明
A proof of a weighted sum conjecture for finite multiple zeta values of level two
AI总结：
本文针对金子真等人提出的二级有限多重zeta值的加权和猜想，通过生成函数、线性递推关系，将问题归约为多项式恒等式，结合Racah型$_4F_3$超几何多项式求解二阶差分方程完成证明。
AI中文摘要：
金子真、村田哲也和吉原明引入了二级有限多重zeta值，并对分量属于{1,2}的指标提出了一个加权和公式的猜想。本文利用生成函数和线性递推关系证明了该猜想，更确切地说，我们将问题归约为一个多项式恒等式，并通过将所得二阶差分方程的特解与Racah型的$_4F_3$超几何多项式对应来求解它。
英文摘要：
M. Kaneko, T. Murakami and A. Yoshihara introduced finite multiple zeta values of level two and conjectured a weighted sum formula for indices whose components belong to $\{1,2\}$. In this paper, we use generating functions and linear recurrence relations to prove the conjecture. More precisely, we reduce the problem to a polynomial identity and solve the resulting second-order difference equation by identifying its specialized solutions with $_4F_3$ hypergeometric polynomials of Racah-type.
