# simple zero

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## 11—20 of 35 matching pages

##### 11: 3.2 Linear Algebra

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►If $\mathbf{A}$ is nondefective and $\lambda $ is a simple zero of ${p}_{n}(\lambda )$, then the sensitivity of $\lambda $ to small perturbations in the matrix $\mathbf{A}$ is measured by the

*condition number*…##### 12: 29.12 Definitions

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►The polynomial $P(\xi )$ is of degree $n$ and has $m$
zeros (all simple) in $(0,1)$ and $n-m$
zeros (all simple) in $(1,{k}^{-2})$.
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##### 13: 19.2 Definitions

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►Let ${s}^{2}(t)$ be a cubic or quartic polynomial in $t$ with simple zeros, and let $r(s,t)$ be a rational function of $s$ and $t$ containing at least one odd power of $s$.
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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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►They are real and distinct, and can be ordered so that ${C}_{p}^{m}(z,\xi )$ and ${S}_{p}^{m}(z,\xi )$ have precisely $m$
zeros, all simple, in $$.
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##### 16: 10.58 Zeros

##### 17: 10.21 Zeros

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►The zeros of any cylinder function or its derivative are simple, with the possible exceptions of $z=0$ in the case of the functions, and $z=0,\pm \nu $ in the case of the derivatives.
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►All of these zeros are simple, provided that $\nu \ge -1$ in the case of ${J}_{\nu}^{\prime}\left(z\right)$, and $\nu \ge -\frac{1}{2}$ in the case of ${Y}_{\nu}^{\prime}\left(z\right)$.
When all of their zeros are simple, the $m$th positive zeros of these functions are denoted by ${j}_{\nu ,m}$, ${j}_{\nu ,m}^{\prime}$, ${y}_{\nu ,m}$, and ${y}_{\nu ,m}^{\prime}$ respectively, except that $z=0$ is counted as the first zero of ${J}_{0}^{\prime}\left(z\right)$.
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►are simple and the asymptotic expansion of the $m$th positive zero as $m\to \mathrm{\infty}$ is given by
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##### 18: 18.2 General Orthogonal Polynomials

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►All $n$
zeros of an OP ${p}_{n}(x)$ are simple, and they are located in the interval of orthogonality $(a,b)$.
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##### 19: 9.12 Scorer Functions

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►All zeros, real or complex, of $\mathrm{Gi}\left(z\right)$ and $\mathrm{Hi}\left(z\right)$ are simple.
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##### 20: Bibliography R

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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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