elementary properties

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21: Bibliography M

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Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications. 3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.

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MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

Ch.14.

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On the interval computation of elementary functions. C. R. Acad. Bulgare Sci. 34 (3), pp. 319–322.

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ISSN 0366-8681, MathReview (David F. Griffiths), ZentralBlatt

Referenced by:

§4.45(i).

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The computation of elementary functions in radix $2^p$ . Computing 53 (3-4), pp. 219–232.

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Notes:

International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993)

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ISSN 0010-485X, Document, MathReview, ZentralBlatt

Referenced by:

§4.45(i).

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An elementary proof of the Macdonald identities for $A_l^{(1)}$ . Adv. in Math. 57 (1), pp. 34–70.

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ISSN 0001-8708, Document, MathReview (Y. Lehrer-Ilamed), ZentralBlatt

Referenced by:

§17.15.

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Elementary Functions: Algorithms and Implementation. Birkhäuser Boston Inc., Boston, MA.

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Notes:

A 2nd edition was published in 2006.

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ISBN 0-8176-3990-X, MathReview (Warren E. Ferguson, Jr.), ZentralBlatt

Referenced by:

§4.45(i).

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22: 19.16 Definitions

… ►Just as the elementary function $R_C(x,y)$ (§19.2(iv)) is the degenerate case … ►The $R$-function is often used to make a unified statement of a property of several elliptic integrals. …

23: Bibliography B

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A monotonicity property involving ${}_3{}^{}F_2^{}$ and comparisons of the classical approximations of elliptical arc length. SIAM J. Math. Anal. 32 (2), pp. 403–419.

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ISSN 1095-7154, Document, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§19.9(i), §19.9(i).

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Integrable Hamiltonian systems and the Painlevé property. Phys. Rev. A (3) 25 (3), pp. 1257–1264.

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ISSN 0556-2791, Document, MathReview

Referenced by:

§32.16.

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Fast multiple-precision evaluation of elementary functions. J. Assoc. Comput. Mach. 23 (2), pp. 242–251.

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Document, MathReview (Amnon Barak), ZentralBlatt

Referenced by:

§4.45(i).

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Discrete Cosine and Sine Transforms. General Properties, Fast Algorithms and Integer Approximations. Elsevier/Academic Press, Amsterdam.

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ISBN 978-0-12-373624-6; 0-12-373624-2, MathReview (Gerd Teschke)

Referenced by:

§18.3.

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24: 2.11 Remainder Terms; Stokes Phenomenon

… ►Two different asymptotic expansions in terms of elementary functions, (2.11.6) and (2.11.7), are available for the generalized exponential integral in the sector . … ►However, to enjoy the resurgence property (§2.7(ii)) we often seek instead expansions in terms of the $F$-functions introduced in §2.11(iii), leaving the connection of the error-function type behavior as an implicit consequence of this property of the $F$-functions. …

25: 2.8 Differential Equations with a Parameter

… ►These are elementary functions in Case I, and Airy functions (§9.2) in Case II. … ►Corresponding to each positive integer $n$ there are solutions $W_{n,j}(u,\xi )$, $j=1,2$, that depend on arbitrarily chosen reference points ${\alpha }_j$, are $C^{\mathrm{\infty }}$ or analytic on $𝚫$, and as $u\to \mathrm{\infty }$ … ►This reference also supplies sufficient conditions to ensure that the solutions $W_{n,1}(u,\xi )$ and $W_{n,2}(u,\xi )$ having the properties (2.8.11) and (2.8.12) are independent of $n$. …

26: Bibliography G

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Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. Phys. 38 (1), pp. 77–81.

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External Links:

MathReview (H. O. Pollak), ZentralBlatt

Referenced by:

§5.6(i), §6.8, §7.8, §8.10.

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Generalized Functions. Vol. 1: Properties and Operations. Academic Press, New York.

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Notes:

Translated from the Russian by Eugene Saletan. A paperbound reprinting by the same publisher appeared in 1977

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MathReview, ZentralBlatt

Referenced by:

§2.6(i).

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Generalized Fermi-Dirac functions and derivatives: Properties and evaluation. Comput. Phys. Comm. 136 (3), pp. 294–309.

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Notes:

Double-precision Fortran, maximum accuracy 20D

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Document, Code, ZentralBlatt

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7th item.

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Do integrable mappings have the Painlevé property?. Phys. Rev. Lett. 67 (14), pp. 1825–1828.

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ISSN 0031-9007, Document, MathReview, ZentralBlatt

Referenced by:

§32.16.

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A monotonicity property of the power function of multivariate tests. Indag. Math. (N.S.) 11 (2), pp. 209–218.

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ISSN 0019-3577, Document, MathReview (Sumitra Purkayastha), ZentralBlatt

Referenced by:

§35.9.

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27: Bibliography L

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Monotonicity properties of zeros of generalized Airy functions. Z. Angew. Math. Phys. 39 (2), pp. 267–271.

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ISSN 0044-2275, Document, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§9.13(i).

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Monotonicity and convexity properties of zeros of Bessel functions. SIAM J. Math. Anal. 8 (1), pp. 171–178.

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ISSN 1095-7154, Document, MathReview (T. Erber), ZentralBlatt

Referenced by:

§10.21(iv).

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Evaluating elementary functions with guaranteed precision. Programming and Computer Software 27 (2), pp. 101–110.

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ISSN 0361-7688, Document, MathReview Entry, ZentralBlatt

Referenced by:

§4.48(ii).

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Elementary solutions of certain Painlevé equations. Differ. Uravn. 1 (3), pp. 731–735 (Russian).

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Notes:

In Russian. English translation: Differential Equations 1(3), pp. 561–564

External Links:

MathReview (Z. Nehari), ZentralBlatt

Referenced by:

§32.10(iii), §32.10(iv), §32.9(i).

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Highly accurate tables for elementary functions. BIT 35 (3), pp. 352–360.

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ISSN 0006-3835, Document, MathReview, ZentralBlatt

Referenced by:

§4.45(i), §4.46.

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