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A criterion is established for the rationality of series of the form Z: &/(a" b * m1 a,) where a" b, are integers, a, 2 2 and lim b,/(a,-,a,) = 0. This criterion is applied to prove irrationality and rational independence of certain special series of the above type.doi:10.2140/pjm.1974.55.85 fatcat:b6q73rzg4zdw5mhxth3fpyfvpi