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11: 28.35 Tables
§28.35 Tables
  • Blanch and Clemm (1969) includes eigenvalues a n ( q ) , b n ( q ) for q = ρ e i ϕ , ρ = 0 ( .5 ) 25 , ϕ = 5 ( 5 ) 90 , n = 0 ( 1 ) 15 ; 4D. Also a n ( q ) and b n ( q ) for q = i ρ , ρ = 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 λ ν ( q ) for General ν
    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 - ( 2 n + 2 ) 2 - q 2 a - ( 2 n ) 2 - q 2 a - ( 2 n - 2 ) 2 - q 2 a - 2 2 = - q 2 ( 2 n + 4 ) 2 - a - q 2 ( 2 n + 6 ) 2 - a - , a = b 2 n + 2 ( q ) .
    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
    λ ν ( q ) .
    16: 28.8 Asymptotic Expansions for Large q
    §28.8 Asymptotic Expansions for Large q
    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.
  • 18: 28.30 Expansions in Series of Eigenfunctions
    28.30.1 w m ′′ + ( λ ^ m + Q ( x ) ) w m = 0 ,
    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.