Honglin ZhuTsinghua University High SchoolJinyi WangTsinghua University High School
S.-T. Yau High School Science Awarded Papersmathscidoc:1702.35010
2016
In this paper we first introduce a fractional form formula among a number
of Euler’s formulas. We then extend the formula and with mathematical
induction prove the case when the number of terms increases and the
exponent is integer. Afterwards, we study the connection between Euler’s
formula and Lagrange interpolating polynomial and use the latter to prove part
of the extended formula. We then obtain a new formula from this connection.
At last, we derive a set of new equations from the extended formula.
@inproceedings{honglin2016the,
title={The Extension of Euler’s Formula and Its Applications},
author={Honglin Zhu, and Jinyi Wang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170227153653415005530},
year={2016},
}
Honglin Zhu, and Jinyi Wang. The Extension of Euler’s Formula and Its Applications. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170227153653415005530.