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A family of Ap\'{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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참고문헌 (13)
참고문헌 신청
/ 1991 / Contests in Higher Mathematics, Mikl´os Schweitzer Competitions 1962-1991. Problem Books in Mathematics / Springer
A. Baker / 1975 / Transcendental Number Theory / Cambridge University Press
A. McGee / 2013 / Cheap talk with two senders and complementary information / Games Econom. Behav 79 : 181 ~ 191
B. C. Berndt / 1977 / Modular transformations and generalizations of several formulae of Ramanujan / Rocky Mountain J. Math 7 (1) : 147 ~ 189
B. C. Berndt / 1978 / Analytic Eisenstein series, theta functions and series relations in the spirit of Ramanujan / J. Reine Angew. Math 303/304 : 332 ~ 365
A. Baker / 1975 / Transcendental Number Theory / Cambridge University Press
A. McGee / 2013 / Cheap talk with two senders and complementary information / Games Econom. Behav 79 : 181 ~ 191
B. C. Berndt / 1977 / Modular transformations and generalizations of several formulae of Ramanujan / Rocky Mountain J. Math 7 (1) : 147 ~ 189
B. C. Berndt / 1978 / Analytic Eisenstein series, theta functions and series relations in the spirit of Ramanujan / J. Reine Angew. Math 303/304 : 332 ~ 365
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