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1: 28.26 Asymptotic Approximations for Large q
§28.26(i) Goldsteins Expansions
2: 28.8 Asymptotic Expansions for Large q
§28.8(iii) Goldsteins Expansions
3: Bibliography G
  • S. Goldstein (1927) Mathieu functions. Trans. Camb. Philos. Soc. 23, pp. 303–336.
  • 4: 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.
  • 5: 28.7 Analytic Continuation of Eigenvalues
    §28.7 Analytic Continuation of Eigenvalues
    The normal values are simple roots of the corresponding equations (28.2.21) and (28.2.22). …See also Mulholland and Goldstein (1929), Bouwkamp (1948), Meixner et al. (1980), Hunter and Guerrieri (1981), Hunter (1981), and Shivakumar and Xue (1999). …
    28.7.4 n = 0 ( b 2 n + 2 ( q ) - ( 2 n + 2 ) 2 ) = 0 .