Arc length of a supercircle equals a series of binomial coefficients times Gauss hypergeometric functions of n and a, specializing at n=2 to a hypergeometric series for π.
Fern ´andez Guasti, A
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On the Arc Length of a Supercircle and a Hypergeometric Formulation of $\pi$
Arc length of a supercircle equals a series of binomial coefficients times Gauss hypergeometric functions of n and a, specializing at n=2 to a hypergeometric series for π.