boundary-value methods or problems

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21: Bibliography J

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The Dirichlet boundary value problem for real solutions of the first Painlevé equation on segments in non-positive semi-axis. J. Reine Angew. Math. 583, pp. 29–86.

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External Links:

ISSN 0075-4102, Document, MathReview (Mehmet Can), ZentralBlatt

Referenced by:

§32.11(i).

Encodings:

BibTeX

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The Painlevé connection problem: An asymptotic approach. I. Stud. Appl. Math. 86 (4), pp. 315–376.

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External Links:

ISSN 0022-2526, MathReview (I. P. Martynov), ZentralBlatt

Referenced by:

§32.11(i), §32.12(ii).

Encodings:

BibTeX

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22: Browsers

… ►Also see About MathML for help for solving problems with MathML in your browser. …

23: 12.15 Generalized Parabolic Cylinder Functions

… ►This equation arises in the study of non-self-adjoint elliptic boundary-value problems involving an indefinite weight function. …

24: 12.16 Mathematical Applications

… ►In Brazel et al. (1992) exponential asymptotics are considered in connection with an eigenvalue problem involving PCFs. …

25: 17.17 Physical Applications

… ►It involves $q$-generalizations of exponentials and Laguerre polynomials, and has been applied to the problems of the harmonic oscillator and Coulomb potentials. …

26: 17.18 Methods of Computation

… ►Shanks (1955) applies such methods in several $q$-series problems; see Andrews et al. (1986).

27: Alexander I. Bobenko

… ►Bobenko’s books are Algebro-geometric Approach to Nonlinear Integrable Problems (with E. …

28: Annie A. M. Cuyt

… ►Her main research interest is in the area of numerical approximation theory and its applications to a diversity of problems in scientific computing. …

29: Hans Volkmer

… ►His book Multiparameter Eigenvalue Problems and Expansion Theorems was published by Springer as Lecture Notes in Mathematics No. …

30: 27.13 Functions

… ►The basic problem is that of expressing a given positive integer $n$ as a sum of integers from some prescribed set $S$ whose members are primes, squares, cubes, or other special integers. …The subsections that follow describe problems from additive number theory. … ►

§27.13(iii) Waring’s Problem

►This problem is named after Edward Waring who, in 1770, stated without proof and with limited numerical evidence, that every positive integer $n$ is the sum of four squares, of nine cubes, of nineteen fourth powers, and so on. Waring’s problem is to find, for each positive integer $k$, whether there is an integer $m$ (depending only on $k$) such that the equation …