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A determinantal approach to irrationality. (English) Zbl 1367.11062
If we want to prove the irrationality of the real number $$\zeta$$ then we usually consider sequences $$\{ p_n\}_{n=1}^\infty$$ and $$\{ q_n\}_{n=1}^\infty$$ of integers such that $$\lim_{n\to\infty}(q_n\zeta - p_n)=0$$ where $$\zeta -\frac{ p_n}{q_n}\not= 0$$ for all positive integers $$n$$. The author of this interesting paper deals with the modification of this method and presents a new proof of the irrationality of the number $$\pi$$ and other numbers. The method makes use of special integrals as well as properties of Hankel and Vandermonde determinants.

MSC:
 11J72 Irrationality; linear independence over a field 30C10 Polynomials and rational functions of one complex variable
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References:
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