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21—30 of 174 matching pages
21: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Oscillatory integrals, Lagrange immersions and unfolding of singularities.
Comm. Pure Appl. Math. 27, pp. 207–281.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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Error bounds for exponentially improved asymptotic solutions of ordinary differential equations having irregular singularities of rank one.
Methods Appl. Anal. 3 (1), pp. 109–134.
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22: 16.21 Differential Equation
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►With the classification of §16.8(i), when the only singularities of (16.21.1) are a regular singularity at and an irregular singularity at .
When the only singularities of (16.21.1) are regular singularities at , , and .
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23: 31.5 Solutions Analytic at Three Singularities: Heun Polynomials
§31.5 Solutions Analytic at Three Singularities: Heun Polynomials
… ►is a polynomial of degree , and hence a solution of (31.2.1) that is analytic at all three finite singularities . …24: Bibliography W
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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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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25: 36.14 Other Physical Applications
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►These are the structurally stable focal singularities (envelopes) of families of rays, on which the intensities of the geometrical (ray) theory diverge.
Diffraction catastrophes describe the (linear) wave amplitudes that smooth the geometrical caustic singularities and decorate them with interference patterns.
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26: 36 Integrals with Coalescing Saddles
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27: Gergő Nemes
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►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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28: Wolter Groenevelt
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►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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