The duplicate form of the Carlitz inversions is employed to prove new identities for terminating balanced \(_4\phi _3\)-series. Their limiting series are deduced as consequences. The “dual formulae” are also derived by means of the polynomial argument.

中文翻译：

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用于终止平衡$$ _ 4 \ phi _3 $$ 4ϕ3-系列的新标识

Carlitz反演的重复形式用于证明终止平衡\（_ 4 \ phi _3 \）-系列的新身份。他们的极限级数被推论为结果。“对偶公式”也可以通过多项式参数得出。