Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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STRUCTURE OF APÉRY-LIKE SERIES AND MONOTONICITY PROPERTIES FOR BINOMIAL SUMS

  • Alkan, Emre (Department of Mathematics Koc University)
  • Received : 2016.01.26
  • Published : 2017.01.31
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Abstract

A family of $Ap{\acute{e}}ry$-like series involving reciprocals of central binomial coefficients is studied and it is shown that they represent transcendental numbers. The structure of such series is further examined in terms of finite combinations of logarithms and arctangents with arguments and coefficients belonging to a suitable algebraic extension of rationals. Monotonicity of certain quotients of weighted binomial sums which arise in the study of competitive cheap talk models is established with the help of a continuous extension of the discrete model at hand. The monotonic behavior of such quotients turns out to have important applications in game theory.

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References

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