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11—20 of 625 matching pages
11: Bibliography D
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The principal frequencies of vibrating systems with elliptic boundaries.
Quart. J. Mech. Appl. Math. 8 (3), pp. 361–372.
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Handbuch der Laplace-Transformation. Bd. II. Anwendungen der Laplace-Transformation. 1. Abteilung.
Birkhäuser Verlag, Basel und Stuttgart (German).
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Inequalities for extreme zeros of some classical orthogonal and -orthogonal polynomials.
Math. Model. Nat. Phenom. 8 (1), pp. 48–59.
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Lamé instantons.
J. High Energy Phys. 2000 (1), pp. Paper 19, 8.
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Uniform asymptotic expansions for Charlier polynomials.
J. Approx. Theory 112 (1), pp. 93–133.
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12: 7.14 Integrals
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7.14.1
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7.14.5
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7.14.7
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►For collections of integrals see Apelblat (1983, pp. 131–146), Erdélyi et al. (1954a, vol. 1, pp. 40, 96, 176–177), Geller and Ng (1971), Gradshteyn and Ryzhik (2000, §§5.4 and 6.28–6.32), Marichev (1983, pp. 184–189), Ng and Geller (1969), Oberhettinger (1974, pp. 138–139, 142–143), Oberhettinger (1990, pp. 48–52, 155–158), Oberhettinger and Badii (1973, pp. 171–172, 179–181), Prudnikov et al. (1986b, vol. 2, pp. 30–36, 93–143), Prudnikov et al. (1992a, §§3.7–3.8), and Prudnikov et al. (1992b, §§3.7–3.8).
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13: Bibliography K
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Pascal program for generating tables of Clebsch-Gordan coefficients.
Comput. Phys. Comm. 85 (1), pp. 82–88.
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Linear convergence and the bisection algorithm.
Amer. Math. Monthly 93 (1), pp. 48–51.
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Special functions and the Bieberbach conjecture.
Amer. Math. Monthly 95 (8), pp. 689–696.
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Estimates of trigonometric sums and their applications.
Uspehi Mat. Nauk 13 (4 (82)), pp. 185–192 (Russian).
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Some special cases of the generalized hypergeometric function
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J. Comput. Appl. Math. 78 (1), pp. 79–95.
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14: 27.2 Functions
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27.2.9
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►It is the special case of the function that counts the number of ways of expressing as the product of factors, with the order of factors taken into account.
…Note that .
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►Table 27.2.2 tabulates the Euler totient function , the divisor function (), and the sum of the divisors (), for .
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15: 3.9 Acceleration of Convergence
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►For further information on the epsilon algorithm see Brezinski and Redivo Zaglia (1991, pp. 78–95).
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Table 3.9.1: Shanks’ transformation for .
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4 | 0.82221 76684 88 | 0.82246 28314 41 | 0.82246 69467 93 | 0.82246 70314 36 | 0.82246 70333 75 |
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8 | 0.82243 73137 33 | 0.82246 67719 32 | 0.82246 70301 49 | 0.82246 70333 73 | 0.82246 70334 23 |
9 | 0.82248 70624 89 | 0.82246 71865 91 | 0.82246 70351 34 | 0.82246 70334 48 | 0.82246 70334 24 |
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16: Bibliography O
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Hyperterminants. II.
J. Comput. Appl. Math. 89 (1), pp. 87–95.
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Uniform asymptotic expansions for hypergeometric functions with large parameters. III.
Analysis and Applications (Singapore) 8 (2), pp. 199–210.
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Connection formulas for second-order differential equations with multiple turning points.
SIAM J. Math. Anal. 8 (1), pp. 127–154.
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On an asymptotic expansion of a ratio of gamma functions.
Proc. Roy. Irish Acad. Sect. A 95 (1), pp. 5–9.
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Numerical evaluation of the dilogarithm of complex argument.
Celestial Mech. Dynam. Astronom. 62 (1), pp. 93–98.
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17: 33.16 Connection Formulas
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§33.16(i) and in Terms of and
… ►where is given by (33.2.5) or (33.2.6). ►§33.16(ii) and in Terms of and when
… ►and again define by (33.14.11) or (33.14.12). … ►and again define by (33.14.11) or (33.14.12). …18: 27.12 Asymptotic Formulas: Primes
19: 1.14 Integral Transforms
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►In this subsection we let .
►If is absolutely integrable on , then is continuous, as , and
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►If and are absolutely integrable on , then so is , and its Fourier transform is , where is the Fourier transform of .
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►If and are continuous and absolutely integrable on , and for all , then for all .
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►In this subsection we let , , , and .
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20: 33.17 Recurrence Relations and Derivatives
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