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In this paper, we investigate the geometric structure of one-cusped L-hypergeometric complex manifolds. By providing explicit constructions, we show how these manifolds arise from a combination of Lhypergeometric functions and specific boundary conditions. Applications of these manifolds are explored in the context of differential equations, number theory, and complex geometry. Numerical examples are provided to illustrate the theoretical results. Mathematics Subject Classification Primary: 32M15, 32J25, 53C55 Secondary: 30F45, 57M50, 22E40
Naidu et al. (Mon,) studied this question.