This research presents an iterative formula to compute π and nested radicals, highlighting implications for mathematical approximation.
In this work, we obtain an iterative formula that can be used for computing digits of π and nested radicals of kind \( c_n/√{2 - cn - 1} \), where c0=0 and \( c_n = √{2 + cn - 1} \). We also show how with help of this iterative formula the two-term Machin-like formulas for π can be generated and approximated. Some examples with Mathematica codes are presented.
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Abrarov et al. (2025) studied this question.
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