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11: 3.2 Linear Algebra
If A is nondefective and λ is a simple zero of p n ( λ ) , then the sensitivity of λ to small perturbations in the matrix A is measured by the condition number
12: 29.12 Definitions
The polynomial P ( ξ ) 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 , ξ ) and S p m ( z , ξ ) have precisely m zeros, all simple, in 0 z < π . …
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 , ± ν in the case of the derivatives. … All of these zeros are simple, provided that ν - 1 in the case of J ν ( z ) , and ν - 1 2 in the case of Y ν ( z ) . When all of their zeros are simple, the m th positive zeros of these functions are denoted by j ν , m , j ν , m , y ν , m , and y ν , m respectively, except that z = 0 is counted as the first zero of J 0 ( z ) . … are simple and the asymptotic expansion of the m th positive zero as m 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 Gi ( z ) and Hi ( z ) 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.