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Talk: Hypergeometric functions, difference equations and Wronskians

Hypergeometric functions, difference equations and Wronskians

Date: 2006..06..14
Event: 16th Orthogonal Polynomials, Special Functions and Applications
Venue: Montreal, Canada

Abstract

There are several ways to prove that a real number \(x\) is irrational. Among them, perhaps the most popular is related to the fact that if \(a_n/b_n\) are rational approximations of \(x\), then both \(a_n\) and \(b_n\) satisfy the same difference equation.

In this talk we will see how it is common for the solutions of this type of difference equations to be hypergeometric functions, and how to apply certain Wronskians to the sequences \(a_n, b_n, ...,\) in order to find suitable rational approximations related to the real number \(x\).

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647 KB Slides (PDF, 18 pages, 40 slides)