# characteristic equation

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## 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 $q=\rho e^{\mathrm{i}\phi}$, $\rho=0(.5)25$, $\phi=5^{\circ}(5^{\circ})90^{\circ}$, $n=0(1)15$; 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.

##### 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 $a-(2n+2)^{2}-\cfrac{q^{2}}{a-(2n)^{2}-\cfrac{q^{2}}{a-(2n-2)^{2}-}}\cdots% \cfrac{q^{2}}{a-2^{2}}=-\cfrac{q^{2}}{(2n+4)^{2}-a-\cfrac{q^{2}}{(2n+6)^{2}-a-% \cdots}},$ $a=b_{2n+2}\left(q\right)$.
##### 14: Bibliography B
• G. Blanch and D. S. Clemm (1969) Mathieu’s Equation for Complex Parameters. Tables of Characteristic Values. U.S. Government Printing Office, Washington, D.C..
• G. Blanch and I. Rhodes (1955) Table of characteristic values of Mathieu’s equation for large values of the parameter. J. Washington Acad. Sci. 45 (6), pp. 166–196.
• W. Bühring (1994) The double confluent Heun equation: Characteristic exponent and connection formulae. Methods Appl. Anal. 1 (3), pp. 348–370.
• ##### 15: 28.1 Special Notation
$\lambda_{\nu}\left(q\right).$
##### 17: Bibliography F
• Y. Fukui and T. Horiguchi (1992) 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.
##### 19: Bibliography L
• W. R. Leeb (1979) Algorithm 537: Characteristic values of Mathieu’s differential equation. ACM Trans. Math. Software 5 (1), pp. 112–117.
• ##### 20: Bibliography M
• H. P. Mulholland and S. Goldstein (1929) The characteristic numbers of the Mathieu equation with purely imaginary parameter. Phil. Mag. Series 7 8 (53), pp. 834–840.