| |
|
|
|
An Elementary Beukers-Like Proof for the Irrationality of π2 |
|
|
|
PP: 35-37 |
|
|
|
Author(s) |
|
|
|
F. M. S. Lima,
P. G. F. Jorda ̃o,
|
|
|
|
Abstract |
|
|
|
In a pioneering work [Bull. London Math. Soc. 11, 268 (1979)], Beukers introduced a simple method, based upon double integrals over the unit-square [0,1]×[0,1] involving Legendre polynomials, for proving the irrationality of ζ(2) and ζ(3). In a more recent paper [Amer. Math. Monthly 108, 222 (2001)], Huylebrouck has adapted the Beukers method for proving the irrationality of π, among other mathematical constants. In this note, we modify Huylebrouck’s proof in order to show the stronger result that π2 is irrational using only single integrals over [0, 1]. |
|
|
|
|
 |
|
