characteristic equation

SearchAdvancedHelp

(0.001 seconds)

11—20 of 30 matching pages

11: 28.35 Tables

§28.35 Tables

… ►

Blanch and Clemm (1969) includes eigenvalues $a_n\left(q\right)$, $b_n\left(q\right)$ for $q=\rho {\mathrm{e}}^{\mathrm{i}\varphi }$, $\rho =0(.5)25$, $\varphi =5^{\circ }(5^{\circ }){90}^{\circ }$, $n=0(1)15$; 4D. Also $a_n\left(q\right)$ and $b_n\left(q\right)$ for $q=\mathrm{i}\rho$, $\rho =0(.5)100$, $n=0(2)14$ and $n=2(2)16$, respectively; 8D. Double points for $n=0(1)15$; 8D. Graphs are included.

…

12: 28.13 Graphics

… ►

§28.13(i) Eigenvalues ${\lambda }_{\nu }\left(q\right)$ for General $\nu$

…

13: 28.6 Expansions for Small $q$

… ►

§28.6(i) Eigenvalues

… ►Higher coefficients in the foregoing series can be found by equating coefficients in the following continued-fraction equations: … ►

28.6.19 $$a-{(2n+2)}^2-\frac{q^2}{a-{(2n)}^2-}\frac{q^2}{a-{(2n-2)}^2-}\mathrm{\cdots }\frac{q^2}{a-2^2}=-\frac{q^2}{{(2n+4)}^2-a-}\frac{q^2}{{(2n+6)}^2-a-}\mathrm{\cdots },$$ $a=b_{2n+2}\left(q\right)$.

ⓘ

Symbols:

$b_n\left(q\right)$: eigenvalues of Mathieu equation, $q=h^2$: parameter, $n$: integer and $a$: parameter

Referenced by:

item (e)

Permalink:

http://dlmf.nist.gov/28.6.E19

Encodings:

pMML, png, TeX

See also:

Annotations for §28.6(i), §28.6 and Ch.28

…

14: Bibliography B

… ►

Mathieu’s Equation for Complex Parameters. Tables of Characteristic Values. U.S. Government Printing Office, Washington, D.C..

ⓘ

External Links:

MathReview (John Todd), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Table of characteristic values of Mathieu’s equation for large values of the parameter. J. Washington Acad. Sci. 45 (6), pp. 166–196.

ⓘ

External Links:

MathReview (L. Fox)

Referenced by:

3rd item.

Encodings:

BibTeX

… ►

The double confluent Heun equation: Characteristic exponent and connection formulae. Methods Appl. Anal. 1 (3), pp. 348–370.

ⓘ

External Links:

ISSN 1073-2772, FullText, MathReview (W. Balser), ZentralBlatt

Referenced by:

§31.12.

Encodings:

BibTeX

…

15: 28.1 Special Notation

… ►

${\lambda }_{\nu }\left(q\right).$

…

16: 28.8 Asymptotic Expansions for Large $q$

§28.8 Asymptotic Expansions for Large $q$

…

17: Bibliography F

… ►

Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice. Phys. A 190 (3-4), pp. 346–362.

ⓘ

External Links:

ISSN 0378-4371, Document, MathReview

Referenced by:

6th item.

Encodings:

BibTeX

…

18: 28.30 Expansions in Series of Eigenfunctions

… ►

28.30.1 $$w_m^{\prime \prime }+({\widehat{\lambda }}_m+Q(x))w_m=0,$$

ⓘ

Symbols:

$m$: integer, $x$: real variable, $w(z)$: Mathieu’s equation solution and ${\widehat{\lambda }}_m$: characteristic values

Permalink:

http://dlmf.nist.gov/28.30.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §28.30(i), §28.30 and Ch.28

…

19: Bibliography L

… ►

Algorithm 537: Characteristic values of Mathieu’s differential equation. ACM Trans. Math. Software 5 (1), pp. 112–117.

ⓘ

External Links:

ISSN 0098-3500, Document, GAMS (module 537; package TOMS)

Referenced by:

2nd item, 2nd item.

Encodings:

BibTeX

…

20: Bibliography M

… ►

The characteristic numbers of the Mathieu equation with purely imaginary parameter. Phil. Mag. Series 7 8 (53), pp. 834–840.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§28.7.

Encodings:

BibTeX

…