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11: 10.23 Sums

… ►The degenerate form of (10.23.8) when $u=\mathrm{\infty }$ is given by …

12: 19.26 Addition Theorems

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13: Bibliography M

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Classical transcendental solutions of the Painlevé equations and their degeneration. Tohoku Math. J. (2) 56 (4), pp. 467–490.

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External Links:

ISSN 0040-8735, Document, MathReview (Oleg Gleizer), ZentralBlatt

Referenced by:

§32.10(v), §32.10(vi).

Encodings:

BibTeX

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14: 1.2 Elementary Algebra

… ►The diagonal elements are not necessarily distinct, and the number of identical (degenerate) diagonal elements is the multiplicity of that specific eigenvalue. …

15: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►If an eigenvalue has multiplicity $>1$, the eigenfunctions may always be orthogonalized in this degenerate sub-space. … ► It is to be noted that if any of the $\lambda \in 𝝈$ have degenerate sub-spaces, that is subspaces of orthogonal eigenfunctions with identical eigenvalues, that in the expansions below all such distinct eigenfunctions are to be included. …

16: 18.39 Applications in the Physical Sciences

… ►which in one dimensional systems are typically non-degenerate, namely there is only a single eigenfunction corresponding to each ${ϵ}_n$, $n\ge 0$. …