Computer aided solution of the invariance equation for two-variable Stolarsky means

Szabolcs Baják, Zsolt Páles

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We solve the so-called invariance equation in the class of two-variable Stolarsky means {Sp q: p, q ε R}, i.e., we find necessary and sufficient conditions on the six parameters a,b,c,d,p,q such that the identity Sp,q(Sa,b(x,y),Sc,d(x,y)) = S p q(x,y) (x,y ε R+), be valid. We recall that, for pq(p - q) ≠ 0 and x ≠y, the Stolarsky mean Sp,qis defined by Sp q(x, y):=(q(xp/p(xq 1/pq In the proof first we approximate the Stolarsky mean and we use the computer-algebra system Maple V Release 9 to compute the Taylor expansion of the approximation up to 12th order, which enables us to describe all the cases of the equality.

Original languageEnglish
Pages (from-to)3219-3227
Number of pages9
JournalApplied Mathematics and Computation
Volume216
Issue number11
DOIs
Publication statusPublished - Aug 1 2010

Keywords

  • Computer algebra
  • Gauss composition
  • Invariance equation
  • Stolarsky mean

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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