rank of singularity
(0.001 seconds)
1—10 of 14 matching pages
1: 31.12 Confluent Forms of Heun’s Equation
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►This has regular singularities at and , and an irregular singularity of rank 1 at .
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►This has irregular singularities at and , each of rank
.
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►This has a regular singularity at , and an irregular singularity at of rank
.
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►This has one singularity, an irregular singularity of rank
at .
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2: 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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3: 2.7 Differential Equations
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§2.7(ii) Irregular Singularities of Rank 1
… ►Thus a regular singularity has rank 0. The most common type of irregular singularity for special functions has rank 1 and is located at infinity. … ►For extensions to singularities of higher rank see Olver and Stenger (1965). … ►For irregular singularities of nonclassifiable rank, a powerful tool for finding the asymptotic behavior of solutions, complete with error bounds, is as follows: …4: 30.2 Differential Equations
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►This equation has regular singularities at with exponents and an irregular singularity of rank 1 at (if ).
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5: 2.9 Difference Equations
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►This situation is analogous to second-order homogeneous linear differential equations with an irregular singularity of rank 1 at infinity (§2.7(ii)).
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6: Bibliography D
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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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7: 33.2 Definitions and Basic Properties
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►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)).
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8: 33.14 Definitions and Basic Properties
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►Again, there is a regular singularity at with indices and , and an irregular singularity of rank 1 at .
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9: Bibliography M
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Hyperasymptotic solutions of second-order ordinary differential equations with a singularity of arbitrary integer rank.
Methods Appl. Anal. 4 (3), pp. 250–260.
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