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1: 28.34 Methods of Computation
§28.34(i) Characteristic Exponents
2: 28.36 Software
§28.36(ii) Characteristic Exponents and Eigenvalues
3: 28.29 Definitions and Basic Properties
§28.29(ii) Floquet’s Theorem and the Characteristic Exponent
Given λ together with the condition (28.29.6), the solutions ± ν of (28.29.9) are the characteristic exponents of (28.29.1). …
4: 28.2 Definitions and Basic Properties
§28.2(iii) Floquet’s Theorem and the Characteristic Exponents
28.2.16 cos ( π ν ) = w I ( π ; a , q ) = w I ( π ; a , q ) .
Either ν ^ or ν is called a characteristic exponent of (28.2.1). …
5: Bibliography B
  • W. Bühring (1994) The double confluent Heun equation: Characteristic exponent and connection formulae. Methods Appl. Anal. 1 (3), pp. 348–370.
  • 6: 3.1 Arithmetics and Error Measures
    A nonzero normalized binary floating-point machine number x is represented as …where s is equal to 1 or 0 , each b j , j 1 , is either 0 or 1 , b 1 is the most significant bit, p ( ) is the number of significant bits b j , b p 1 is the least significant bit, E is an integer called the exponent, b 0 . b 1 b 2 b p 1 is the significand, and f = . b 1 b 2 b p 1 is the fractional part. … Let E min E E max with E min < 0 and E max > 0 . For given values of E min , E max , and p , the format width in bits N of a computer word is the total number of bits: the sign (one bit), the significant bits b 1 , b 2 , , b p 1 ( p 1 bits), and the bits allocated to the exponent (the remaining N p bits). The integers p , E min , and E max are characteristics of the machine. …
    7: Bibliography M
  • mpmath (free python library)
  • 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.
  • H. J. W. Müller (1962) Asymptotic expansions of oblate spheroidal wave functions and their characteristic numbers. J. Reine Angew. Math. 211, pp. 33–47.
  • H. J. W. Müller (1963) Asymptotic expansions of prolate spheroidal wave functions and their characteristic numbers. J. Reine Angew. Math. 212, pp. 26–48.
  • H. J. W. Müller (1966a) Asymptotic expansions of ellipsoidal wave functions and their characteristic numbers. Math. Nachr. 31, pp. 89–101.
  • 8: 2.7 Differential Equations
    Let α 1 , α 2 denote the indices or exponents, that is, the roots of the indicial equationwhere λ 1 , λ 2 are the roots of the characteristic equationSee §2.11(v) for other examples. … The transformed differential equation either has a regular singularity at t = , or its characteristic equation has unequal roots. … This is characteristic of numerically satisfactory pairs. …