• Corpus ID: 119696723

Very accurate approximations for the elliptic integrals of the second kind in terms of Stolarsky means

  title={Very accurate approximations for the elliptic integrals of the second kind in terms of Stolarsky means},
  author={Zhen-Hang Yang},
  journal={arXiv: Classical Analysis and ODEs},
  • Zhen-Hang Yang
  • Published 22 August 2015
  • Mathematics
  • arXiv: Classical Analysis and ODEs
For $a,b>0$ with $a\neq b$, the Stolarsky means are defined by% \begin{equation*} S_{p,q}\left(a,b\right) =\left({\dfrac{q(a^{p}-b^{p})}{p(a^{q}-b^{q})}}% \right) ^{1/(p-q)}\text{if}pq\left(p-q\right) \neq 0 \end{equation*}% and $S_{p,q}\left(a,b\right) $ is defined as its limits at $p=0$ or $q=0$ or $p=q$ if $pq\left(p-q\right) =0$. The complete elliptic integrals of the second kind $E$ is defined on $\left(0,1\right) $ by% \begin{equation*} E\left(r\right) =\int_{0}^{\pi /2}\sqrt{1-r^{2}\sin… 
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