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New bounds for the exponential function with cotangent.

Ling Zhu1

  • 1Department of Mathematics, Zhejiang Gongshang University, Hangzhou, China.

Journal of Inequalities and Applications
|May 18, 2018
PubMed
Summary
This summary is machine-generated.

Researchers established new bounds for the exponential function involving cotangent. This was achieved using power series expansions and a novel monotonicity criterion for quotients of power series.

Keywords:
BoundsCircular functionsInequalities

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Area of Science:

  • Mathematical Analysis
  • Number Theory

Background:

  • The exponential function and cotangent are fundamental in various mathematical and scientific fields.
  • Estimating the behavior of functions using power series is a common analytical technique.

Purpose of the Study:

  • To derive novel, rigorous bounds for the exponential function incorporating cotangent.
  • To introduce and apply a new criterion for analyzing the monotonicity of power series quotients.

Main Methods:

  • Utilizing the recurrence relation between coefficients in the power series expansion of the exponential function.
  • Applying a newly developed criterion for the monotonicity of the quotient of two power series.

Main Results:

  • New bounds for the exponential function with cotangent have been successfully determined.
  • The efficacy of the new monotonicity criterion was demonstrated through its application.

Conclusions:

  • The study successfully provides new analytical bounds for a specific function combination.
  • The findings contribute to the understanding of function approximation and monotonicity analysis in series expansions.