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Apéry's Rational Approximation to His Constant


	R. Apéry used a rapidly converging rational approximation to ζ(3) 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.


	Contributed by: Oleksandr Pavlyk

Many other rapidly convergent rational approximations to ζ(3) have been given since the original article of Apéry.

Apéry's Constant (Wolfram MathWorld)

Riemann Zeta Function (Wolfram MathWorld)

Irrational Number (Wolfram MathWorld)

"Apéry's Rational Approximation to His Constant" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/AperysRationalApproximationToHisConstant/

Contributed by: Oleksandr Pavlyk

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