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\\mathbb{N}^*}$, where the infinite lower-triangular matrix $A(x,\\nu)$ and its inverse $B(x,\\nu)$ involve Hypergeometric polynomials $F(\\cdot)$, namely $$\n  \\left\\{\n  \\begin{array}{ll}\n  A_{n,k}(x,\\nu) = \\displaystyle (-1)^k\\binom{n}{k}F(k-n,-n\\nu;-n;x),\n  \\\\\n  B_{n,k}(x,\\nu) = \\displaystyle (-1)^k\\binom{n}{k}F(k-n,k\\nu;k;x)\n  \\end{array} \\right. $$ for $1 \\leqslant k 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