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- W2215277203 abstract "We examine series of the form $$sum_{n=0}^infty {2n choose n}^{-1} frac{(4x^2)^n}{2n+2m+1} textrm{and} sum_{n=0}^infty {2n choose n}^{-1} frac{(-4x^2)^n}{2n+2m+1} .$$ In each case, there is an evaluation of the form $(p_m (x) f(x) - q_m (x))/x^{2m}$ where $f(x)$ is a transcendental function and $p_m (x)$ and $q_m (x)$ are polynomials with rational coefficients. We prove that for $vert x vert lt 1$, $$lim_{m to infty} frac{q_m (x)}{p_m (x)} = f(x) .$$ From this result, we derive recurrences for $pi$ and for various logarithms." @default.
- W2215277203 created "2016-06-24" @default.
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- W2215277203 date "2013-05-01" @default.
- W2215277203 modified "2023-09-30" @default.
- W2215277203 title "On the Limiting Structure of Some Central Binomial Evaluations" @default.
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- W2215277203 doi "https://doi.org/10.35834/mjms/1369746393" @default.
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