# simple zero

(0.002 seconds)

## 11—20 of 35 matching pages

##### 11: 3.2 Linear Algebra
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
The polynomial $P(\xi)$ is of degree $n$ and has $m$ zeros (all simple) in $(0,1)$ and $n-m$ zeros (all simple) in $(1,k^{-2})$. …
##### 13: 19.2 Definitions
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 $s$. …
##### 14: 2.8 Differential Equations with a Parameter
In Case II $f(z)$ has a simple zero at $z_{0}$ and $g(z)$ is analytic at $z_{0}$. …
##### 15: 28.31 Equations of Whittaker–Hill and Ince
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 $0\leq z<\pi$. …
##### 16: 10.58 Zeros
However, there are no simple relations that connect the zeros of the derivatives. …
##### 17: 10.21 Zeros
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. … All of these zeros are simple, provided that $\nu\geq-1$ in the case of $J_{\nu}'\left(z\right)$, and $\nu\geq-\tfrac{1}{2}$ in the case of $Y_{\nu}'\left(z\right)$. When all of their zeros are simple, the $m$th positive zeros of these functions are denoted by $j_{\nu,m}$, ${j^{\prime}_{\nu,m}}$, $y_{\nu,m}$, and ${y^{\prime}_{\nu,m}}$ respectively, except that $z=0$ is counted as the first zero of $J_{0}'\left(z\right)$. … are simple and the asymptotic expansion of the $m$th positive zero as $m\to\infty$ is given by …
##### 18: 18.2 General Orthogonal Polynomials
All $n$ zeros of an OP $p_{n}(x)$ are simple, and they are located in the interval of orthogonality $(a,b)$. …
##### 19: 9.12 Scorer Functions
All zeros, real or complex, of $\mathrm{Gi}\left(z\right)$ and $\mathrm{Hi}\left(z\right)$ are simple. …
##### 20: Bibliography R
• Hans-J. Runckel (1971) On the zeros of the hypergeometric function. Math. Ann. 191 (1), pp. 53–58.
• J. Rushchitsky and S. Rushchitska (2000) 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.