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Apéry's Rational Approximation to His Constant

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R. Apéry used a rapidly converging rational approximation to to prove its irrationality. Both numerator and denominator satisfy the same recurrence equation , with initial conditions , , , and . Approximately three decimal digits are gained with each degree. The notation means digits have been left out.

Contributed by: Oleksandr Pavlyk (March 2011)
Open content licensed under CC BY-NC-SA

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Many other rapidly convergent rational approximations to have been given since Apéry's original article.

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