characteristic polynomial
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1: 3.2 Linear Algebra
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►is called the characteristic polynomial of and its zeros are the eigenvalues of .
The multiplicity of an eigenvalue is its multiplicity as a zero of the characteristic polynomial (§3.8(i)).
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►Its characteristic polynomial can be obtained from the recursion
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3.2.23
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2: 28.34 Methods of Computation
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(f)
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3: 21.7 Riemann Surfaces
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►where is a polynomial in and that does not factor over .
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§21.7(ii) Fay’s Trisecant Identity
… ► ►§21.7(iii) Frobenius’ Identity
… ►where is a polynomial in of odd degree . …4: Bibliography L
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Algorithm 537: Characteristic values of Mathieu’s differential equation.
ACM Trans. Math. Software 5 (1), pp. 112–117.
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The real zeros of the Bernoulli polynomials.
J. Approx. Theory 58 (2), pp. 124–150.
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On the maxima and minima of Bernoulli polynomials.
Amer. Math. Monthly 47 (8), pp. 533–538.
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Approximation of orthogonal polynomials in terms of Hermite polynomials.
Methods Appl. Anal. 6 (2), pp. 131–146.
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Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials.
J. Math. Anal. Appl. 239 (2), pp. 457–477.
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5: Bibliography B
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The generating function of Jacobi polynomials.
J. London Math. Soc. 13, pp. 8–12.
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A generalisation of the Legendre polynomial.
Proc. London Math. Soc. (2) 3 (3), pp. 111–123.
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Mathieu’s Equation for Complex Parameters. Tables of Characteristic Values.
U.S. Government Printing Office, Washington, D.C..
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Table of characteristic values of Mathieu’s equation for large values of the parameter.
J. Washington Acad. Sci. 45 (6), pp. 166–196.
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The double confluent Heun equation: Characteristic exponent and connection formulae.
Methods Appl. Anal. 1 (3), pp. 348–370.
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6: Bibliography F
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II.
J. Math. Anal. Appl. 7 (3), pp. 440–451.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order.
J. Math. Anal. Appl. 6 (3), pp. 394–403.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. III.
J. Math. Anal. Appl. 12 (3), pp. 593–601.
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Polynomial relations in the Heisenberg algebra.
J. Math. Phys. 35 (11), pp. 6144–6149.
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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.
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7: Bibliography
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Some orthogonal -polynomials.
Math. Nachr. 30, pp. 47–61.
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Zeros of Stieltjes and Van Vleck polynomials.
Trans. Amer. Math. Soc. 252, pp. 197–204.
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Frequency response characteristics of the multiport planar elliptic patch.
IEEE Trans. Microwave Theory Tech. 40 (8), pp. 1726–1730.
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A primer on Bernoulli numbers and polynomials.
Math. Mag. 81 (3), pp. 178–190.
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Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials.
Mem. Amer. Math. Soc. 54 (319), pp. iv+55.
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8: Bibliography C
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A note on Euler numbers and polynomials.
Nagoya Math. J. 7, pp. 35–43.
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Stability properties of disk polynomials.
Numer. Algorithms.
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Properties of generalized Freud polynomials.
J. Approx. Theory 225, pp. 148–175.
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The fourth Painlevé equation and associated special polynomials.
J. Math. Phys. 44 (11), pp. 5350–5374.
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Algorithm 352: Characteristic values and associated solutions of Mathieu’s differential equation.
Comm. ACM 12 (7), pp. 399–407.
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