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This paper introduces a closed-form transcendental formulation that converges monotonically to ๐. The expression is constructed by evaluating a base-10 sequence featuring a terminal digit 9 collapsing toward zero within the arccosine function. The formulation analytically converges to ๐ in the limit as the exponent index approaches infinity.
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Bheema Varanasi (2026) studied this question.
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