The Extension of Euler’s Formula and Its Applications

Honglin Zhu Tsinghua University High School Jinyi Wang Tsinghua University High School

S.-T. Yau High School Science Awarded Papers mathscidoc:1702.35010

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.
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  title={The Extension of Euler’s Formula and Its Applications},
  author={Honglin Zhu, and Jinyi Wang},
Honglin Zhu, and Jinyi Wang. The Extension of Euler’s Formula and Its Applications. 2016.
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