# coalescing peak and endpoint

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## 4 matching pages

##### 1: 2.3 Integrals of a Real Variable

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###### §2.3(v) Coalescing Peak and Endpoint: Bleistein’s Method

…##### 2: 2.4 Contour Integrals

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►The problem of obtaining an asymptotic approximation to $I(\alpha ,z)$ that is uniform with respect to $\alpha $ in a region containing $\widehat{\alpha}$ is similar to the problem of a coalescing endpoint and saddle point outlined in §2.3(v).
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►The problems sketched in §§2.3(v) and 2.4(v) involve only two of many possibilities for the coalescence of endpoints, saddle points, and singularities in integrals associated with the special functions.
…For a coalescing saddle point and endpoint see Olver (1997b, Chapter 9) and Wong (1989, Chapter 7); if the endpoint is an algebraic singularity then the uniform approximants are parabolic cylinder functions with fixed parameter, and if the endpoint is not a singularity then the uniform approximants are complementary error functions.
►For two coalescing saddle points and an endpoint see Leubner and Ritsch (1986).
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##### 3: 7.20 Mathematical Applications

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►For applications of the complementary error function in uniform asymptotic approximations of integrals—saddle point coalescing with a pole or saddle point coalescing with an endpoint—see Wong (1989, Chapter 7), Olver (1997b, Chapter 9), and van der Waerden (1951).
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##### 4: Bibliography L

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A note on the uniform asymptotic expansion of integrals with coalescing endpoint and saddle points.
J. Phys. A 19 (3), pp. 329–335.
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