PlanetMath: Apéry's constant

(more info)

Math for the people, by the people.

donor list - find out how

Main Menu

Apéry's constant

(Definition)

$\displaystyle \zeta(3)$	$\displaystyle = \sum_{n=1}^\infty\frac{1}{n^3}$
	$\displaystyle = 1.202056903159594285399738161511449990764986292\ldots$

has been called Apéry's constant since 1979, when Roger Apéry published a remarkable proof that it is irrational [1].

References

1: Roger Apéry.
Irrationalité de $\zeta(2)$ et $\zeta(3)$ .
Astérisque, 61:11-13, 1979.
2: Alfred van der Poorten.
A proof that Euler missed. Apéry's proof of the irrationality of $\zeta(3)$ . An informal report.
Math. Intell., 1:195-203, 1979.

"Apéry's constant" is owned by bbukh. [ full author list (2) | owner history (1) ]

(view preamble | get metadata)

This object's parent.

Log in to rate this entry.
(view current ratings)

Cross-references: irrational, proof, number
There are 2 references to this entry.

This is version 5 of Apéry's constant, born on 2003-02-11, modified 2003-10-22.
Object id is 4021, canonical name is AperysConstant.
Accessed 3282 times total.

Classification:

AMS MSC:	11M06 (Number theory :: Zeta and $L$-functions: analytic theory :: $\zeta $)
	11J81 (Number theory :: Diophantine approximation, transcendental number theory :: Transcendence )

Pending Errata and Addenda

None.[ View all 1 ]

Discussion

forum policy

No messages.

Interact