Approximation of values of hypergeometric functions by restricted rationals
Carsten Elsner, Takao Komatsu, Iekata Shiokawa (2007)
Journal de Théorie des Nombres de Bordeaux
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We compute upper and lower bounds for the approximation of hyperbolic functions at points by rationals , such that satisfy a quadratic equation. For instance, all positive integers with solving the Pythagorean equation satisfy Conversely, for every there are infinitely many coprime integers , such that and hold simultaneously for some integer . A generalization to the approximation of for rational...