This analysis discusses rational and meromorphic solutions in q-difference equations, suggesting new conditions and examples.
We are concerned with q-difference equations of second order with polynomial coefficients. By means of characteristic equations and recurrence relations of formal series, we discuss rational solutions and transcendental meromorphic solutions. We will consider the solutions under a certain condition that has not been sufficiently studied. Further, we discuss reducible conditions for the second-order equations and we will propose some examples.
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SUZUKI et al. (2025) studied this question.
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