distributional methods
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21—26 of 26 matching pages
21: 25.10 Zeros
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§25.10(i) Distribution
… ►In the region , called the critical strip, has infinitely many zeros, distributed symmetrically about the real axis and about the critical line . … ►Riemann developed a method for counting the total number of zeros of in that portion of the critical strip with . …22: Bibliography G
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On high precision methods for computing integrals involving Bessel functions.
Math. Comp. 33 (147), pp. 1049–1057.
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On the generalization of a method for computing Bessel function integrals.
J. Comput. Appl. Math. 6 (2), pp. 167–168.
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Quasirandom distributed bases for bound problems.
J. Chem. Phys. 114 (9), pp. 3929–3939.
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A method for evaluating certain Bessel integrals.
Z. Angew. Math. Phys. 30 (4), pp. 722–723.
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Spectral Methods and Their Applications.
World Scientific Publishing Co. Inc., River Edge, NJ-Singapore.
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23: Bibliography S
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A method of generating integral relations by the simultaneous separability of generalized Schrödinger equations.
SIAM J. Math. Anal. 10 (4), pp. 823–838.
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Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation.
Adv. Quantum Chem. 72, pp. 95–127.
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A global Newton method for the zeros of cylinder functions.
Numer. Algorithms 18 (3-4), pp. 259–276.
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Practical Extrapolation Methods: Theory and Applications.
Cambridge Monographs on Applied and Computational Mathematics, Vol. 10, Cambridge University Press, Cambridge.
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A Guide to Distribution Theory and Fourier Transforms.
Studies in Advanced Mathematics, CRC Press, Boca Raton, FL.
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24: 1.11 Zeros of Polynomials
25: Bibliography H
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Sur la distribution des zéros de la fonction et ses conséquences arithmétiques.
Bull. Soc. Math. France 24, pp. 199–220 (French).
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The combination of -matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr.
J. Phys. B 26 (12), pp. 1775–1790.
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On the distribution of the zeros of generalized Airy functions.
Math. Comp. 29 (131), pp. 863–877.
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Algorithm 395: Student’s t-distribution.
Comm. ACM 13 (10), pp. 617–619.
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Algorithm 571: Statistics for von Mises’ and Fisher’s distributions of directions: , and their inverses [S14].
ACM Trans. Math. Software 7 (2), pp. 233–238.
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26: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►of the Dirac delta distribution.
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►For a formally self-adjoint second order differential operator , such as that of (1.18.28), the space can be seen to consist of all such that the distribution
can be identified with a function in , which is the function .
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►The reader is referred to Coddington and Levinson (1955), Friedman (1990, Ch. 3), Titchmarsh (1962a), and Everitt (2005b, pp. 45–74) and Everitt (2005a, pp. 272–331), for detailed methods and results.
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