irregular pairs
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1: 24.19 Methods of Computation
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►For number-theoretic applications it is important to compute for ; in particular to find the irregular pairs
for which .
We list here three methods, arranged in increasing order of efficiency.
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2: 33.22 Particle Scattering and Atomic and Molecular Spectra
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►For scattering problems, the interior solution is then matched to a linear combination of a pair of Coulomb functions, and , or and , to determine the scattering -matrix and also the correct normalization of the interior wave solutions; see Bloch et al. (1951).
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3: 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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►(28.2.1) possesses a fundamental pair of solutions called basic solutions with
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4: 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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►As in the case of differential equations (§§2.7(iii), 2.7(iv)) recessive solutions are unique and dominant solutions are not; furthermore, one member of a numerically satisfactory pair has to be recessive.
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