isolated singularity
(0.001 seconds)
31—40 of 87 matching pages
31: 10.2 Definitions
…
►
§10.2(i) Bessel’s Equation
… ►This differential equation has a regular singularity at with indices , and an irregular singularity at of rank ; compare §§2.7(i) and 2.7(ii). …32: 31.3 Basic Solutions
…
►In general, one of them has a logarithmic singularity at .
►
§31.3(ii) Fuchs–Frobenius Solutions at Other Singularities
… ►Solutions (31.3.1) and (31.3.5)–(31.3.11) comprise a set of 8 local solutions of (31.2.1): 2 per singular point. …33: Bibliography
…
►
Unsteady lifting-line theory as a singular-perturbation problem.
J. Fluid Mech 153, pp. 59–81.
…
►
Scattering by singular potentials with a perturbation – Theoretical introduction to Mathieu functions.
J. Mathematical Phys. 16, pp. 961–970.
…
►
Singularities of Differentiable Maps. Vol. II.
Birkhäuser, Boston-Berlin.
►
Normal forms of functions near degenerate critical points, the Weyl groups and Lagrangian singularities.
Funkcional. Anal. i Priložen. 6 (4), pp. 3–25 (Russian).
…
►
Singular Continuous Spectrum for a Class of Almost Periodic Jacobi Matrices.
Bulletin of the American Mathematical Society 6 (1), pp. 81–85.
…
34: 15.19 Methods of Computation
…
►However, since the growth near the singularities of the differential equation is algebraic rather than exponential, the resulting instabilities in the numerical integration might be tolerable in some cases.
…
35: 21.7 Riemann Surfaces
…
►This compact curve may have singular points, that is, points at which the gradient of vanishes.
Removing the singularities of this curve gives rise to a two-dimensional connected manifold with a complex-analytic structure, that is, a Riemann
surface. All compact Riemann surfaces can be obtained this
way.
…
►On this surface, we choose
cycles (that is, closed oriented curves, each with at most a finite number of singular points) , , , such that their intersection indices satisfy
…
►Thus the differentials , have no singularities on .
…
36: 33.2 Definitions and Basic Properties
…
►
§33.2(i) Coulomb Wave Equation
… ►This differential equation has a regular singularity at with indices and , and an irregular singularity of rank 1 at (§§2.7(i), 2.7(ii)). …37: 33.14 Definitions and Basic Properties
…
►
§33.14(i) Coulomb Wave Equation
… ►Again, there is a regular singularity at with indices and , and an irregular singularity of rank 1 at . …38: 31.11 Expansions in Series of Hypergeometric Functions
…
►and (31.11.1) converges to (31.3.10) outside the ellipse in the -plane with foci at 0, 1, and passing through the third finite singularity at .
►Every Heun function (§31.4) can be represented by a series of Type I convergent in the whole plane cut along a line joining the two singularities of the Heun function.
…
►The expansion (31.11.1) with (31.11.12) is convergent in the plane cut along the line joining the two singularities
and .
…
39: Bibliography S
…
►
Euler-Maclaurin expansions for integrals with endpoint singularities: A new perspective.
Numer. Math. 98 (2), pp. 371–387.
►
A simple approach to asymptotic expansions for Fourier integrals of singular functions.
Appl. Math. Comput. 216 (11), pp. 3378–3385.
…
►
Euler-Maclaurin expansions for integrals with arbitrary algebraic endpoint singularities.
Math. Comp. 81 (280), pp. 2159–2173.
►
Euler-Maclaurin expansions for integrals with arbitrary algebraic-logarithmic endpoint singularities.
Constr. Approx. 36 (3), pp. 331–352.
…
►
Operators with Singular Continuous Spectrum: I. General Operators.
Annals of Mathematics 141 (1), pp. 131–145.
…