Some Properties Of Generalized Agard Distortion,Gamma And Other Special Functions

This thesis is divided into four chapters as follows.In the first chapter, we introduce the research background of this thesis and some nota-tions used in this paper.In the second chapter, we present some monotonicity and convexity properties of the classical gamma, beta and psi functions. By these results, some new asymptotically sharp estimates of these special functions are obtained and several known results are improved or generalized. At the same time, we show some monotonicity and concavity properties of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In addition, applying the new results for the psi function, the authors improve the well-known lower and upper bounds for the approximate evaluation of Euler’s constant γ.In the third chapter, by showing the monotonicity properties of certain combinations of the generalized Agard distortion function ηk(a, t) and the generalized linear distortion function λ(a, K) with some elementary functions, we obtain several properties of functions ηk(a, t) and λ(a, K), by which several new inequalities are derived.In the fourth chapter, we elaborate the work about this paper and research ideas in the future.