fundamental solutions

SearchAdvancedHelp

(0.002 seconds)

11—20 of 25 matching pages

11: 13.14 Definitions and Basic Properties

… ►

§13.14(v) Numerically Satisfactory Solutions

►Fundamental pairs of solutions of (13.14.1) that are numerically satisfactory (§2.7(iv)) in the neighborhood of infinity are … ►A fundamental pair of solutions that is numerically satisfactory in the sector $|\mathrm{ph}z|\le \pi$ near the origin is …

12: 16.21 Differential Equation

… ►A fundamental set of solutions of (16.21.1) is given by …

13: Bibliography S

… ►

Relations among the fundamental solutions of the generalized hypergeometric equation when $p=q+1$. II. Logarithmic cases. Bull. Amer. Math. Soc. 45 (12), pp. 927–935.

ⓘ

External Links:

Document, MathReview (C. S. Meijer), ZentralBlatt

Referenced by:

§16.8(ii).

Encodings:

BibTeX

…

14: Bibliography C

… ►

Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems. SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 042, 26.

ⓘ

External Links:

ISSN 1815-0659, Document, MathReview (Heinrich Begehr), ZentralBlatt

Referenced by:

§14.28(ii), §14.28(ii).

Encodings:

BibTeX

…

15: 29.7 Asymptotic Expansions

… ►Müller (1966a, b) found three formal asymptotic expansions for a fundamental system of solutions of (29.2.1) (and (29.11.1)) as $\nu \to \mathrm{\infty }$, one in terms of Jacobian elliptic functions and two in terms of Hermite polynomials. …

16: 4.37 Inverse Hyperbolic Functions

… ►

§4.37(v) Fundamental Property

►With $k\in \mathbb{Z}$, the general solutions of the equations …

17: 4.23 Inverse Trigonometric Functions

… ►

§4.23(v) Fundamental Property

►With $k\in \mathbb{Z}$, the general solutions of the equations …

18: 18.39 Applications in the Physical Sciences

… ►The fundamental quantum Schrödinger operator, also called the Hamiltonian, $\mathscr{H}$, is a second order differential operator of the form … ►The solutions of (18.39.8) are subject to boundary conditions at $a$ and $b$. … ►The solutions (18.39.8) are called the stationary states as separation of variables in (18.39.9) yields solutions of form … ►Brief mention of non-unit normalized solutions in the case of mixed spectra appear, but as these solutions are not OP’s details appear elsewhere, as referenced. … ►The radial Coulomb wave functions $R_{n,l}(r)$, solutions of …

19: 27.14 Unrestricted Partitions

… ►A fundamental problem studies the number of ways $n$ can be written as a sum of positive integers $\le n$, that is, the number of solutions of …

20: 18.38 Mathematical Applications

… ►

Differential Equations: Spectral Methods

… ►Classical OP’s play a fundamental role in Gaussian quadrature. … ►Schneider et al. (2016) discuss DVR/Finite Element solutions of the time-dependent Schrödinger equation. … ►It has elegant structures, including $N$-soliton solutions, Lax pairs, and Bäcklund transformations. … ►has a solution …