positive%20definite
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11—20 of 349 matching pages
11: Bibliography W
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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On the points of inflection of Bessel functions of positive order. II.
Canad. J. Math. 43 (3), pp. 628–651.
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On uniform asymptotic expansion of definite integrals.
J. Approximation Theory 7 (1), pp. 76–86.
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12: 35.6 Confluent Hypergeometric Functions of Matrix Argument
13: 20 Theta Functions
Chapter 20 Theta Functions
…14: 35.2 Laplace Transform
15: 19.31 Probability Distributions
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►More generally, let () and () be real positive-definite matrices with rows and columns, and let be the eigenvalues of .
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16: 26.2 Basic Definitions
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►If the set consists of the integers 1 through , a permutation can be thought of as a rearrangement of these integers where the integer in position
is .
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►A partition of a nonnegative integer
is an unordered collection of positive integers whose sum is .
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17: 18.40 Methods of Computation
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►In what follows we consider only the simple, illustrative, case that is continuously differentiable so that , with real, positive, and continuous on a real interval The strategy will be to: 1) use the moments to determine the recursion coefficients of equations (18.2.11_5) and (18.2.11_8); then, 2) to construct the quadrature abscissas and weights (or Christoffel numbers) from the J-matrix of §3.5(vi), equations (3.5.31) and(3.5.32).
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►A simple set of choices is spelled out in Gordon (1968) which gives a numerically stable algorithm for direct computation of the recursion coefficients in terms of the moments, followed by construction of the J-matrix and quadrature weights and abscissas, and we will follow this approach: Let be a positive integer and define
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18.40.2
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18.40.3
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►Results of low ( to decimal digits) precision for are easily obtained for to .
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18: 9.11 Products
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§9.11(iii) Integral Representations
… ►For , , , where is any positive integer, see Albright (1977). … ►§9.11(v) Definite Integrals
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9.11.19
►For further definite integrals see Prudnikov et al. (1990, §1.8.2), Laurenzi (1993), Reid (1995, 1997a, 1997b), and Vallée and Soares (2010, Chapters 3, 4).
19: Guide to Searching the DLMF
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Table 1: Query Examples
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proximity operator:
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Query | Matching records contain |
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int_$^$ sin |
any definite integral of sin |
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adj, prec/n, and near/n, where n is any positive natural number.