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algebraic Lamé functions

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1: 29.17 Other Solutions
§29.17(ii) Algebraic Lamé Functions
Algebraic Lamé functions are solutions of (29.2.1) when ν is half an odd integer. …
2: Bibliography E
  • A. Erdélyi (1941c) On algebraic Lamé functions. Philos. Mag. (7) 32, pp. 348–350.
  • 3: 31.8 Solutions via Quadratures
    For m = ( m 0 , 0 , 0 , 0 ) , these solutions reduce to Hermite’s solutions (Whittaker and Watson (1927, §23.7)) of the Lamé equation in its algebraic form. …
    4: 29 Lamé Functions
    Chapter 29 Lamé Functions
    5: 1 Algebraic and Analytic Methods
    Chapter 1 Algebraic and Analytic Methods
    6: 14 Legendre and Related Functions
    Chapter 14 Legendre and Related Functions
    7: 29.22 Software
    §29.22(i) Lamé Functions
  • LA1: Eigenvalues for Lamé functions.

  • LA2: Lamé functions.

  • Program LA5 uses symbolic algebra.
    §29.22(ii) Lamé Polynomials
    8: 10 Bessel Functions
    Chapter 10 Bessel Functions
    9: 18 Orthogonal Polynomials
    10: 31.7 Relations to Other Functions
    §31.7(i) Reductions to the Gauss Hypergeometric Function
    Joyce (1994) gives a reduction in which the independent variable is transformed not polynomially or rationally, but algebraically.
    §31.7(ii) Relations to Lamé Functions
    equation (31.2.1) becomes Lamé’s equation with independent variable ζ ; compare (29.2.1) and (31.2.8). The solutions (31.3.1) and (31.3.5) transform into even and odd solutions of Lamé’s equation, respectively. …