numerical integration
(0.002 seconds)
31—40 of 43 matching pages
31: Bibliography B
…
►
Numerical calculation of a generalized complete elliptic integral.
Rev. Mod. Phys. 10, pp. 264–269.
…
►
Numerical Methods for Least Squares Problems.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
…
►
Numerical evaluation of continued fractions.
SIAM Rev. 6 (4), pp. 383–421.
…
►
Numerical aspects of Mathieu eigenvalues.
Rend. Circ. Mat. Palermo (2) 15, pp. 51–97.
…
►
Numerical calculation of elliptic integrals and elliptic functions.
Numer. Math. 7 (1), pp. 78–90.
…
32: 19.15 Advantages of Symmetry
…
►The function (Carlson (1963)) reveals the full permutation symmetry that is partially hidden in , and leads to symmetric standard integrals that simplify many aspects of theory, applications, and numerical computation.
…
►Symmetry makes possible the reduction theorems of §19.29(i), permitting remarkable compression of tables of integrals while generalizing the interval of integration.
…These reduction theorems, unknown in the Legendre theory, allow symbolic integration without imposing conditions on the parameters and the limits of integration (see §19.29(ii)).
…
33: Mourad E. H. Ismail
…
►Ismail has published numerous papers on special functions, orthogonal polynomials, approximation theory, combinatorics, asymptotics, and related topics.
…
►Ismail serves on several editorial boards including the Cambridge University Press book series Encyclopedia of Mathematics and its Applications, and on the editorial boards of 9 journals including Proceedings of the American Mathematical Society (Integrable Systems and Special Functions Editor); Constructive
Approximation; Journal of Approximation Theory; and Integral Transforms
and Special Functions.
…
34: 2.11 Remainder Terms; Stokes Phenomenon
…
►
§2.11(i) Numerical Use of Asymptotic Expansions
… ►By integration by parts (§2.3(i)) … ►§2.11(vi) Direct Numerical Transformations
… ►The numerically smallest terms are the 5th and 6th. … ►However, direct numerical transformations need to be used with care. …35: 22.19 Physical Applications
…
►The classical rotation of rigid bodies in free space or about a fixed point may be described in terms of elliptic, or hyperelliptic, functions if the motion is integrable (Audin (1999, Chapter 1)).
…
►Numerous other physical or engineering applications involving Jacobian elliptic functions, and their inverses, to problems of classical dynamics, electrostatics, and hydrodynamics appear in Bowman (1953, Chapters VII and VIII) and Lawden (1989, Chapter 5).
…
36: 18.40 Methods of Computation
…
►Usually, however, other methods are more efficient, especially the numerical solution of difference equations (§3.6) and the application of uniform asymptotic expansions (when available) for OP’s of large degree.
…
►
A numerical approach to the recursion coefficients and quadrature abscissas and weights
… ►There are many ways to implement these first two steps, noting that the expressions for and of equation (18.2.30) are of little practical numerical value, see Gautschi (2004) and Golub and Meurant (2010). 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 …See Gautschi (1983) for examples of numerically stable and unstable use of the above recursion relations, and how one can then usefully differentiate between numerical results of low and high precision, as produced thereby. …37: 25.11 Hurwitz Zeta Function
…
►
25.11.6
, , .
►
25.11.7
, , , .
…
►
25.11.19
, , .
…
►
25.11.30
, ,
►where the integration contour is a loop around the negative real axis as described for (25.5.20).
…
38: 6.16 Mathematical Applications
…
►By integration by parts
…
39: 9.12 Scorer Functions
…
►
§9.12(iv) Numerically Satisfactory Solutions
► is a numerically satisfactory companion to the complementary functions and on the interval . … ►In , numerically satisfactory sets of solutions are given by … ►where the integration contour separates the poles of from those of . … ►For the above properties and further results, including the distribution of complex zeros, asymptotic approximations for the numerically large real or complex zeros, and numerical tables see Gil et al. (2003c). …40: Bibliography N
…
►
Numerical Algorithms Group, Ltd..
…
►
Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes.
ACM Trans. Math. Software 18 (3), pp. 345–349.
►
Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes.
J. Comput. Appl. Math. 39 (2), pp. 193–200.
…
►
On the numerical evaluation of the generalised Fermi-Dirac integrals.
Comput. Phys. Comm. 76 (1), pp. 48–50.
…
►
Bisection hardly ever converges linearly.
Numer. Math. 70 (1), pp. 111–118.
…