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1: Bibliography C

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Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.

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External Links:

ISSN 0174-4747, MathReview (F. T. Howard), ZentralBlatt

Referenced by:

§26.8(vii).

Encodings:

BibTeX

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Algorithm 597: Sequence of modified Bessel functions of the first kind. ACM Trans. Math. Software 9 (2), pp. 242–245.

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Notes:

Double-precision Fortran, maximum accuracy 24S.

External Links:

ISSN 0098-3500, Document, GAMS (module 597; package TOMS), ZentralBlatt

Referenced by:

5th item.

Encodings:

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Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§13.29(v), §15.19(v).

Encodings:

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Department of Computer Science, University of Victoria, Canada.

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Notes:

Permutations, set and integer partitions, sequences, graphs, and trees.

External Links:

Combinatorial Object Server

Referenced by:

1st item.

Encodings:

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A sequence of series for the Lambert $W$ function. In Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), pp. 197–204.

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External Links:

Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

(4.13.4_1), (4.13.4_2), (4.13.5_2), §4.13.

Encodings:

BibTeX

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2: 3.8 Nonlinear Equations

… ►Let $z_1,z_2,\mathrm{\dots }$ be a sequence of approximations to a root, or fixed point, $\zeta$. …for all $n$ sufficiently large, where $A$ and $p$ are independent of $n$, then the sequence is said to have convergence of the $p$th order. … ►For real functions $f(x)$ the sequence of approximations to a real zero $\xi$ will always converge (and converge quadratically) if either: … ►Consider $x=20$ and $j=19$. We have $p^{\prime }(20)=19!$ and $a_{19}=1+2+\mathrm{\cdots }+20=210$. …

3: Bibliography S

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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean. SIAM J. Math. Anal. 20 (6), pp. 1514–1528.

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External Links:

ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§22.19(i), §22.20(vi).

Encodings:

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Non-linear transformations of divergent and slowly convergent sequences. J. Math. Phys. 34, pp. 1–42.

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External Links:

MathReview (J. Kuntzmann), ZentralBlatt

Referenced by:

§17.18.

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Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

Encodings:

BibTeX

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The On-Line Encyclopedia of Integer Sequences. Notices Amer. Math. Soc. 50 (8), pp. 912–915.

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External Links:

ISSN 0002-9920, FullText, Electronic Database, MathReview (Christian Krattenthaler), ZentralBlatt

Referenced by:

(19.20.2), (19.20.22), (19.30.13), (25.11.40), (3.12.1), (3.12.3), (3.12.4), §3.12, (4.2.11), (4.2.17), (4.2.18), (4.4.19), (5.17.6), (5.2.3), (5.4.10), (5.4.6), (5.4.7), (5.4.8), (5.4.9), (6.13.1).

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A Maple package for symmetric functions. J. Symbolic Comput. 20 (5-6), pp. 755–768.

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Notes:

For software see John Stembridge’s home page. The SF package contains Maple software for zonal, Jack, and Macdonald polynomials.

External Links:

Home Page, ISSN 0747-7171, Document, MathReview, ZentralBlatt

Referenced by:

3rd item.

Encodings:

BibTeX

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4: 1.11 Zeros of Polynomials

… ►Resolvent cubic is $z^3+12z^2+20z+9=0$ with roots ${\theta }_1=-1$, ${\theta }_2=-\frac{1}{2}(11+\sqrt{85})$, ${\theta }_3=-\frac{1}{2}(11-\sqrt{85})$, and $\sqrt{-{\theta }_1}=1$, $\sqrt{-{\theta }_2}=\frac{1}{2}(\sqrt{17}+\sqrt{5})$, $\sqrt{-{\theta }_3}=\frac{1}{2}(\sqrt{17}-\sqrt{5})$. … ►where the column vector $h_k^{(m)}$ consists of the first $k$ members of the sequence $a_m,a_{m-1},a_{m-2},\mathrm{\dots }$ with $a_j=0$ if or $j>n$. …