regularization
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11: 33.12 Asymptotic Expansions for Large
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33.12.2
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33.12.3
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33.12.6
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►For asymptotic expansions of and when see Temme (2015, Chapter 31).
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►Then, by application of the results given in §§2.8(iii) and 2.8(iv), two sets of asymptotic expansions can be constructed for and when .
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12: 33.6 Power-Series Expansions in
13: 33.15 Graphics
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14: 33.17 Recurrence Relations and Derivatives
15: 33.18 Limiting Forms for Large
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16: 33.14 Definitions and Basic Properties
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§33.14(i) Coulomb Wave Equation
… ►Again, there is a regular singularity at with indices and , and an irregular singularity of rank 1 at . … ►§33.14(ii) Regular Solution
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33.14.4
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33.14.5
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17: 33.11 Asymptotic Expansions for Large
18: 31.12 Confluent Forms of Heun’s Equation
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►Confluent forms of Heun’s differential equation (31.2.1) arise when two or more of the regular singularities merge to form an irregular singularity.
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►This has regular singularities at and , and an irregular singularity of rank 1 at .
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►This has a regular singularity at , and an irregular singularity at of rank .
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19: 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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