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31: Bibliography M

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Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.

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External Links:

ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§10.74(iii).

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An improved calculation of the general elliptic integral of the second kind in the neighbourhood of $x=0$ . Numer. Math. 25 (1), pp. 99–101.

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ISSN 0029-599X, Document, MathReview (Roland Bulirsch), ZentralBlatt

Referenced by:

§19.36(ii).

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BibTeX

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Calculation of zeros of cylindrical functions and their derivatives. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. (2), pp. 63–64, 71 (Russian).

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Notes:

In Russian

External Links:

ISSN 0137-0782, MathReview, ZentralBlatt

Referenced by:

§10.74(vi).

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Calculation of the complete elliptic integrals with complex modulus. Numer. Math. 29 (2), pp. 233–236.

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Notes:

An Algol procedure for calculating the complete elliptic integrals of the first and the second kind with complex modulus $k$ is included.

External Links:

ISSN 0029-599X, Document, MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§19.36(ii), §19.39(ii).

Encodings:

BibTeX

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SciFace Software, Paderborn, Germany.

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Notes:

Computer algebra system for doing symbolic and exact algebraic computations as well as numerical calculations with almost arbitrary accuracy

Referenced by:

§ ‣ Software Cross Index.

Encodings:

BibTeX

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32: Bibliography G

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A note on the recursive calculation of incomplete gamma functions. ACM Trans. Math. Software 25 (1), pp. 101–107.

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External Links:

ISSN 0098-3500, Document, MathReview Entry, ZentralBlatt

Referenced by:

§8.25(v).

Encodings:

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Calculation of Gauss quadrature rules. Math. Comp. 23 (106), pp. 221–230.

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Notes:

Loose microfiche suppl. A1–A10

External Links:

FullText, MathReview (F. Stenger), ZentralBlatt

Referenced by:

§18.39(iii), §3.5(vi).

Encodings:

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Inductance Calculations. Van Nostrand, New York.

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Notes:

Reprinted by Dover, New York, 1962 and 2004

External Links:

ZentralBlatt

Referenced by:

§19.34.

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33: 27.14 Unrestricted Partitions

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§27.14(iii) Asymptotic Formulas

►These recursions can be used to calculate $p\left(n\right)$, which grows very rapidly. …

34: Bibliography H

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On an “equivalent quadrature” calculation of matrix elements of ${(z-p^2/2m)}^{-1}$ using an $L^2$ expansion technique. J. Comput. Phys. 13, pp. 536–550.

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External Links:

Document, Link

Referenced by:

§18.39(iv).

Encodings:

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Calculation of Coulomb wave functions for high energies. Phys. Rev. 54 (8), pp. 627–628.

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External Links:

Document

Referenced by:

§33.7.

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35: 3.1 Arithmetics and Error Measures

… ►Interval arithmetic is intended for bounding the total effect of rounding errors of calculations with machine numbers. … ►During the calculations common divisors are removed from the rational numbers, and the final results can be converted to decimal representations of arbitrary length. …

36: 22.20 Methods of Computation

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§22.20(iv) Lattice Calculations

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37: Bibliography N

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On the calculation of elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 91–94.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§19.36(ii).

Encodings:

BibTeX

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38: 3.11 Approximation Techniques

… ► Moreover, the set of minimax approximations $p_0(x),p_1(x),p_2(x),\mathrm{\dots },p_n(x)$ requires the calculation and storage of $\frac{1}{2}(n+1)(n+2)$ coefficients, whereas the corresponding set of Chebyshev-series approximations requires only $n+1$ coefficients. ►

Calculation of Chebyshev Coefficients

►The $c_n$ in (3.11.11) can be calculated from (3.11.10), but in general it is more efficient to make use of the orthogonal property (3.11.9). … ►A widely implemented and used algorithm for calculating the coefficients $p_j$ and $q_j$ in (3.11.16) is Remez’s second algorithm. …

39: 12.11 Zeros

… ►Numerical calculations in this case show that $z_{\frac{1}{2},s}$ corresponds to the $s$th zero on the string; compare §7.13(ii). …

40: 30.16 Methods of Computation

… ►The coefficients $a_{n,k}^m({\gamma }^2)$ calculated in §30.16(ii) can be used to compute $S_n^{m(j)}(z,\gamma )$, $j=1,2,3,4$ from (30.11.3) as well as the connection coefficients $K_n^m(\gamma )$ from (30.11.10) and (30.11.11). …