tailieunhanh - Lecture Analytic combinatorics (Part 2) - Chapter 8: Saddle-point asymptotics
A saddle-point of a surface is a point reminiscent of the inner part of a saddle or of a geographical pass between two mountains. If the surface represents the modulus of an analytic function, saddle-points are simply determined as the zeros of the derivative of the function. This chapter presents the following content: Modulus surfaces, saddle point bounds, saddle point asymptotics, applications. | ANALYTIC COMBINATORICS PART TWO http 8. Saddle-Point Asymptotics Analytic combinatorics overview A. SYMBOLIC METHOD 1. OGFs 2. EGFs 3. MGFs B. COMPLEX ASYMPTOTICS 4. Rational Meromorphic 5. Applications of R M 6. Singularity Analysis 7. Applications of SA 8. Saddle point specification SYMBOLIC METHOD GF equation COMPLEX ASYMPTOTICS asymptotic estimate T desired result 2 ANALYTIC COMBINATORICS PART TWO http CAMBRIDGE Analytic Combinatorics Philippe Flajolet and Robert Sedgewick 8. Saddle-Point Asymptotics Modulus surfaces Saddle point bounds Saddle point asymptotics Applications .
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