simple zero
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11: 3.2 Linear Algebra
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βΊIf is nondefective and is a simple zero of , then the sensitivity of to small perturbations in the matrix is measured by the condition number
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12: 29.12 Definitions
13: 19.2 Definitions
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βΊLet be a cubic or quartic polynomial in with simple zeros, and let be a rational function of and containing at least one odd power of .
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14: 2.8 Differential Equations with a Parameter
15: 28.31 Equations of Whittaker–Hill and Ince
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βΊThey are real and distinct, and can be ordered so that and have precisely
zeros, all simple, in .
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16: 10.58 Zeros
17: 10.21 Zeros
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βΊThe zeros of any cylinder function or its derivative are simple, with the possible exceptions of in the case of the functions, and in the case of the derivatives.
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βΊAll of these zeros are simple, provided that in the case of , and in the case of .
When all of their zeros are simple, the th positive zeros of these functions are denoted by , , , and respectively, except that is counted as the first zero of .
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βΊare simple and the asymptotic expansion of the th positive zero as is given by
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18: 9.12 Scorer Functions
19: 18.2 General Orthogonal Polynomials
20: Bibliography R
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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (4), pp. 91.
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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (3), pp. 56–64.
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On the zeros of the hypergeometric function.
Math. Ann. 191 (1), pp. 53–58.
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On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media.
In Differential Operators and Related Topics, Vol. I (Odessa,
1997),
Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.
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