Lagrange%20inversion%20theorem
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11: 27.15 Chinese Remainder Theorem
§27.15 Chinese Remainder Theorem
… ►This theorem is employed to increase efficiency in calculating with large numbers by making use of smaller numbers in most of the calculation. …Their product has 20 digits, twice the number of digits in the data. By the Chinese remainder theorem each integer in the data can be uniquely represented by its residues (mod ), (mod ), (mod ), and (mod ), respectively. …These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result , which is correct to 20 digits. …12: 2.2 Transcendental Equations
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►where and () is the coefficient of in the asymptotic expansion of (Lagrange’s formula for the reversion of
series).
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13: Bibliography G
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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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On mean convergence of extended Lagrange interpolation.
J. Comput. Appl. Math. 43 (1-2), pp. 19–35.
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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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A theorem on the numerators of the Bernoulli numbers.
Amer. Math. Monthly 97 (2), pp. 136–138.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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14: Peter L. Walker
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►Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004.
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15: 8 Incomplete Gamma and Related
Functions
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16: 28 Mathieu Functions and Hill’s Equation
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17: Bibliography L
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Démonstration d’un Théoréme d’Arithmétique.
Nouveau Mém. Acad. Roy. Sci. Berlin, pp. 123–133 (French).
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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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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