eigenvalues (or characteristic values)
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31—40 of 87 matching pages
31: 29.1 Special Notation
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►All derivatives are denoted by differentials, not by primes.
►The main functions treated in this chapter are the eigenvalues
, , , , the Lamé functions , , , , and the Lamé polynomials , , , , , , , .
The notation for the eigenvalues and functions is due to Erdélyi et al. (1955, §15.5.1) and that for the polynomials is due to Arscott (1964b, §9.3.2).
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►Other notations that have been used are as follows: Ince (1940a) interchanges with .
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32: 30.9 Asymptotic Approximations and Expansions
§30.9 Asymptotic Approximations and Expansions
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30.9.1
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►The asymptotic behavior of and as in descending powers of is derived in Meixner (1944).
…The behavior of for complex and large is investigated in Hunter and Guerrieri (1982).
33: 30.7 Graphics
34: 28.4 Fourier Series
35: 28.29 Definitions and Basic Properties
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►iff is an eigenvalue of the matrix
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§28.29(iii) Discriminant and Eigenvalues in the Real Case
… ►To every equation (28.29.1), there belong two increasing infinite sequences of real eigenvalues: ►
28.29.16
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28.29.17
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36: Hans Volkmer
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►His book Multiparameter Eigenvalue Problems and Expansion Theorems was published by Springer as Lecture Notes in Mathematics No.
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37: 3.7 Ordinary Differential Equations
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§3.7(iv) Sturm–Liouville Eigenvalue Problems
… ►The Sturm–Liouville eigenvalue problem is the construction of a nontrivial solution of the system …The values are the eigenvalues and the corresponding solutions of the differential equation are the eigenfunctions. The eigenvalues are simple, that is, there is only one corresponding eigenfunction (apart from a normalization factor), and when ordered increasingly the eigenvalues satisfy … ►The larger the absolute values of the eigenvalues that are being sought, the smaller the integration steps need to be. …38: 28.8 Asymptotic Expansions for Large
39: 19.31 Probability Distributions
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►More generally, let () and () be real positive-definite matrices with rows and columns, and let be the eigenvalues of .
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19.31.2
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