regular singularity
(0.001 seconds)
11—20 of 24 matching pages
11: 33.2 Definitions and Basic Properties
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§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)). …12: 13.2 Definitions and Basic Properties
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►This equation has a regular singularity at the origin with indices and , and an irregular singularity at infinity of rank one.
…In effect, the regular singularities of the hypergeometric differential equation at and coalesce into an irregular singularity at .
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13: 14.2 Differential Equations
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►Equation (14.2.2) has regular singularities at , , and , with exponent pairs , , and , respectively; compare §2.7(i).
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14: 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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15: Bibliography B
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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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16: 28.2 Definitions and Basic Properties
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►This equation has regular singularities at 0 and 1, both with exponents 0 and , and an irregular singular point at .
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17: 13.14 Definitions and Basic Properties
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►It has a regular singularity at the origin with indices , and an irregular singularity at infinity of rank one.
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18: 1.16 Distributions
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►(If a distribution is not regular, it is called singular.)
More generally, for a nondecreasing function the corresponding Lebesgue–Stieltjes measure (see §1.4(v)) can be considered as a distribution:
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19: 15.10 Hypergeometric Differential Equation
20: 31.14 General Fuchsian Equation
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►The general second-order Fuchsian equation with
regular singularities at , , and at , is given by
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