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11—20 of 124 matching pages
11: 21.1 Special Notation
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positive integers. | |
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complex, symmetric matrix with strictly positive definite, i.e., a Riemann matrix. | |
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12: 10.37 Inequalities; Monotonicity
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►If
is fixed, then throughout the interval , is positive and increasing, and is positive and decreasing.
►If
is fixed, then throughout the interval , is decreasing, and is increasing.
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13: 23.20 Mathematical Applications
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►The boundary of the rectangle , with vertices , , , , is mapped strictly monotonically by onto the real line with , , , , .
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►The two pairs of edges and of are each mapped strictly monotonically by onto the real line, with , , ; similarly for the other pair of edges.
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14: 8 Incomplete Gamma and Related
Functions
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15: 28 Mathieu Functions and Hill’s Equation
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16: Bibliography G
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A new application of the discrete Laguerre polynomials in the numerical evaluation of the Hankel transform of a strongly decreasing even function.
J. Comput. Phys. 42 (2), pp. 277–287.
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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17: 18.40 Methods of Computation
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►Given the power moments, , , can these be used to find a unique , a non-decreasing, real, function of , in the case that the moment problem is determined? Should a unique solution not exist the moment problem is then indeterminant.
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►Results of low ( to decimal digits) precision for are easily obtained for to .
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18: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
19: 23 Weierstrass Elliptic and Modular
Functions
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20: 36 Integrals with Coalescing Saddles
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