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Applications of a class of transformations of complex sequences

John M. Campbell
Dec 2022
摘要
Through an application of a remarkable result due to Mishev in 2018concerning the inverses for a class of transformations of sequences of complexnumbers, we obtain a very simple proof for a famous series for $\frac{1}{\pi}$due to Ramanujan. We then apply Mishev's transform to provide proofs for anumber of related hypergeometric identities, including a new and simplifiedproof for a family of series for $\frac{1}{\pi}$ previously obtained by Levrievia Fourier--Legendre theory. We generalize this result using Mishev'stransform, so as to extend a result due to Guillera on a Ramanujan-like seriesinvolving cubed binomial coefficients and harmonic numbers.
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