A transcendence measure for \(\pi^ 2\). (English. Russian original) Zbl 0876.11035

Sorokin, V. N.

Sb. Math. 187, No. 12, 1819-1852 (1996); translation from Mat. Sb. 187, No. 12, 87-120 (1996).

The paper deals with a new proof of the transcendence of the number \(\pi\). This proof is based on the generalization of the Hermite method. The so-called Beukers integrals are used too. The measure of the transcendence of the number \(\pi^2\) is included.

Reviewer: J.Hančl (Ostrava)

MSC:

11J82	Measures of irrationality and of transcendence
11J72	Irrationality; linear independence over a field
41A21	Padé approximation

Keywords:

transcendence measure; transcendence of \(\pi\); Hermite method; Beukers integrals