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41—50 of 87 matching pages
41: Bibliography B
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Unfolding the high orders of asymptotic expansions with coalescing saddles: Singularity theory, crossover and duality.
Proc. Roy. Soc. London Ser. A 443, pp. 107–126.
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Singularities in Waves and Rays.
In Les Houches Lecture Series Session XXXV, R. Balian, M. Kléman, and J.-P. Poirier (Eds.),
Vol. 35, pp. 453–543.
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Uniform asymptotic expansions of integrals with stationary point near algebraic singularity.
Comm. Pure Appl. Math. 19, pp. 353–370.
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Uniform asymptotic expansions of integrals with many nearby stationary points and algebraic singularities.
J. Math. Mech. 17, pp. 533–559.
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Uniform asymptotic solutions of a class of second-order linear differential equations having a turning point and a regular singularity, with an application to Legendre functions.
SIAM J. Math. Anal. 17 (2), pp. 422–450.
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42: 1.13 Differential Equations
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§1.13(vi) Singularities
►For classification of singularities of (1.13.1) and expansions of solutions in the neighborhoods of singularities, see §2.7. …43: 2.4 Contour Integrals
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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.
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►For two coalescing saddle points and an algebraic singularity see Temme (1986), Jin and Wong (1998).
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44: 10.47 Definitions and Basic Properties
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►Equations (10.47.1) and (10.47.2) each have a regular singularity at with indices , , and an irregular singularity at of rank ; compare §§2.7(i)–2.7(ii).
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45: 20.13 Physical Applications
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►In the singular limit , the functions , , become integral kernels of Feynman path integrals (distribution-valued Green’s functions); see Schulman (1981, pp. 194–195).
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46: 28.7 Analytic Continuation of Eigenvalues
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►The only singularities are algebraic branch points, with and finite at these points.
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47: Bibliography F
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Numerical calculation of singular integrals related to Hankel transform.
Comput. Math. Appl. 21 (2-3), pp. 87–94.
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Singularity analysis of generating functions.
SIAM J. Discrete Math. 3 (2), pp. 216–240.
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48: Bibliography W
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Asymptotic expansions of Fourier transforms of functions with logarithmic singularities.
J. Math. Anal. Appl. 64 (1), pp. 173–180.
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Asymptotic expansions of Hankel transforms of functions with logarithmic singularities.
Comput. Math. Appl. 3 (4), pp. 271–286.
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49: 15.2 Definitions and Analytical Properties
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§15.2(ii) Analytic Properties
…50: Bibliography E
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The Fuchsian equation of second order with four singularities.
Duke Math. J. 9 (1), pp. 48–58.
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