Asymptotic Methods in AnalysisAn original, effective approach teaches by explaining worked examples in detail. "Every step in the mathematical process is explained, its purpose and necessity made clear . . . the reader not only has no difficulty in following the rigorous proofs, but even turns to them with eager expectation." — Nuclear Physics. 1981 edition. |
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analysis analytic function apply approximation argument assume asymptotic behaviour asymptotic expansion asymptotic formula asymptotic information asymptotic series b₁ bounded coefficients complex conformal mapping consider converges defined denote depends derivative differential equation discuss E. C. TITCHMARSH E. T. Whittaker easily seen equals estimate Euler-Maclaurin Euler-Maclaurin formula evaluate example exists finite fixed fn(x follows formal function f G. N. WATSON give half-plane highest point infer integrand integration path interval iteration Laplace method log log N. G. DE BRUIJN neighbourhood O-formulas O(log obtain positive constant positive number power series problem proved real axis real number remark replace result Riccati equation right-hand-side Rouché theorem saddle point method satisfies sequence sinn solution p(t substitution t₁ Tauberian tends theorem theory upper half-plane variable whence Xn+1 zero ἐπ