isolated singularity
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21—30 of 87 matching pages
21: Bibliography O
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Exponentially improved asymptotic solutions of ordinary differential equations. II Irregular singularities of rank one.
Proc. Roy. Soc. London Ser. A 445, pp. 39–56.
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Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one.
Proc. Roy. Soc. London Ser. A 454, pp. 1–29.
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Error bounds for asymptotic solutions of second-order differential equations having an irregular singularity of arbitrary rank.
J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 244–249.
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On the asymptotic solution of second-order differential equations having an irregular singularity of rank one, with an application to Whittaker functions.
J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 225–243.
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Asymptotic solutions of linear ordinary differential equations at an irregular singularity of rank unity.
Methods Appl. Anal. 4 (4), pp. 375–403.
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22: 14.21 Definitions and Basic Properties
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§14.21(iii) Properties
… ►This includes, for example, the Wronskian relations (14.2.7)–(14.2.11); hypergeometric representations (14.3.6)–(14.3.10) and (14.3.15)–(14.3.20); results for integer orders (14.6.3)–(14.6.5), (14.6.7), (14.6.8), (14.7.6), (14.7.7), and (14.7.11)–(14.7.16); behavior at singularities (14.8.7)–(14.8.16); connection formulas (14.9.11)–(14.9.16); recurrence relations (14.10.3)–(14.10.7). …23: 15.17 Mathematical Applications
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►The three singular points in Riemann’s differential equation (15.11.1) lead to an interesting Riemann sheet structure.
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24: 31.6 Path-Multiplicative Solutions
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►This denotes a set of solutions of (31.2.1) with the property that if we pass around a simple closed contour in the -plane that encircles and once in the positive sense, but not the remaining finite singularity, then the solution is multiplied by a constant factor .
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25: 14.8 Behavior at Singularities
26: 31.4 Solutions Analytic at Two Singularities: Heun Functions
§31.4 Solutions Analytic at Two Singularities: Heun Functions
…27: 36.6 Scaling Relations
28: 29.2 Differential Equations
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►This equation has regular singularities at the points , where , and , are the complete elliptic integrals of the first kind with moduli , , respectively; see §19.2(ii).
In general, at each singularity each solution of (29.2.1) has a branch point (§2.7(i)).
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29: 31.2 Differential Equations
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31.2.1
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►This equation has regular singularities at , with corresponding exponents , , , , respectively (§2.7(i)).
All other homogeneous linear differential equations of the second order having four regular singularities in the extended complex plane, , can be transformed into (31.2.1).
►The parameters play different roles: is the singularity parameter; are exponent parameters; is the accessory parameter.
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