Apéry's constant: Difference between revisions

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This constant was known and studied by many early mathematicians, but was not named until 1978, after Roger Apéry who was first to prove it was an irrational number.

This constant was known and studied by many early mathematicians, but was not named until 1978, after Roger Apéry, who was first to prove it was an irrational number.

<math>\zeta(3)</math> is easy to calculate, but it converges very slowly. The first 1000 terms are only accurate to 6 decimal places.

<math>\zeta(3)</math> by summing reciprocal cubes is easy to calculate, but converges very slowly. The first 1000 terms are only accurate to 6 decimal places.

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;* Show the value of Apéry's constant calculated at least three different ways.

;:# Show the value of at least the first 1000 terms of <math>\zeta(3)</math> direct ~~calculation~~ truncated to 100 decimal digits.

;:# Show the value of at least the first 1000 terms of <math>\zeta(3)</math> by direct summing of reciprocal cubes, truncated to 100 decimal digits.

;:# Show the value of the first 158 terms of Markov / Apéry representation truncated to 100 decimal digits.

;:# Show the value of the first 20 terms of Wedeniwski representation truncated to 100 decimal digits.