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<p>Motivated by Van Hamme’s (C.2) supercongruence and several of its generalizations due to Jana, Karmakar and Kalita, we establish <i>q</i>-analogues of some known supercongruences via the <i>q</i>-Zeilberger algorithm. Moreover, we derive parametric generalizations of these <i>q</i>-supercongruences. In particular, by constructing suitable rational functions, we obtain several new <i>q</i>-supercongruences related to (C.2).</p>

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q-Analogues of Some Supercongruences Related to the (C.2) Supercongruence of Van Hamme

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Song-Xiao Li,
  • Su-Dan Wang

摘要

Motivated by Van Hamme’s (C.2) supercongruence and several of its generalizations due to Jana, Karmakar and Kalita, we establish q-analogues of some known supercongruences via the q-Zeilberger algorithm. Moreover, we derive parametric generalizations of these q-supercongruences. In particular, by constructing suitable rational functions, we obtain several new q-supercongruences related to (C.2).