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21: Bibliography V

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J. Van Deun and R. Cools (2008) Integrating products of Bessel functions with an additional exponential or rational factor. Comput. Phys. Comm. 178 (8), pp. 578–590.

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Notes:: Associated computer program available online
External Links:: ISSN 0010-4655, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §10.74(vii), §10.74(vii).
Encodings:: BibTeX

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P. Verbeeck (1970) Rational approximations for exponential integrals

E_{n}(x)

. Acad. Roy. Belg. Bull. Cl. Sci. (5) 56, pp. 1064–1072.

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External Links:: MathReview (A. Magnus), ZentralBlatt
Referenced by:: 3rd item.
Encodings:: BibTeX

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22: Bibliography U

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Unpublished Mathematical Tables (1944) Mathematics of Computation Unpublished Mathematical Tables Collection.

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Notes:: Archives of American Mathematics, Center for American History, The University of Texas at Austin. Covers 1944–1994. An online guide is arranged chronologically by date of issuance within Mathematics of Computation
External Links:: Guide
Referenced by:: §27.21.
Encodings:: BibTeX

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… ►Most notably, he served as the Editor-in-Chief and Mathematics Editor of the online NIST Digital Library of Mathematical Functions and its 966-page print companion, the NIST Handbook of Mathematical Functions (Cambridge University Press, 2010). …

24: Bibliography M

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I. G. Macdonald (1990) Hypergeometric Functions.

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Notes:: Unpublished Lecture Notes, University of London. An online version exists.
External Links:: FullText
Referenced by:: §35.7(ii), §35.8(iii).
Encodings:: BibTeX

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B. Markman (1965) Contribution no. 14. The Riemann zeta function. BIT 5, pp. 138–141.

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Referenced by:: §25.21(ii).
Encodings:: BibTeX

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L. C. Maximon (1991) On the evaluation of the integral over the product of two spherical Bessel functions. J. Math. Phys. 32 (3), pp. 642–648.

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External Links:: ISSN 0022-2488, Document, MathReview (S. K. Chatterjea), ZentralBlatt
Referenced by:: §1.17(ii), §10.59.
Encodings:: BibTeX

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J. W. Meijer and N. H. G. Baken (1987) The exponential integral distribution. Statist. Probab. Lett. 5 (3), pp. 209–211.

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External Links:: ISSN 0167-7152, Document, MathReview Entry, ZentralBlatt
Referenced by:: §8.19(xi).
Encodings:: BibTeX

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J. Meixner (1951) Klassifikation, Bezeichnung und Eigenschaften der Sphäroidfunktionen. Math. Nachr. 5, pp. 1–18 (German).

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External Links:: Document, MathReview (F. Oberhettinger), ZentralBlatt
Referenced by:: §30.10.
Encodings:: BibTeX

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25: Bibliography D

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G. M. D’Ariano, C. Macchiavello, and M. G. A. Paris (1994) Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A 50 (5), pp. 4298–4302.

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External Links:: Document
Referenced by:: §13.28(iii).
Encodings:: BibTeX

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K. Dilcher, L. Skula, and I. Sh. Slavutskiǐ (1991) Bernoulli Numbers. Bibliography (1713–1990). Queen’s Papers in Pure and Applied Mathematics, Vol. 87, Queen’s University, Kingston, ON.

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Notes:: A frequently updated version, with links to reviews, exists online
External Links:: Online version, MathReview, ZentralBlatt
Referenced by:: Ch.24.
Encodings:: BibTeX

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A. M. Din (1981) A simple sum formula for Clebsch-Gordan coefficients. Lett. Math. Phys. 5 (3), pp. 207–211.

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External Links:: ISSN 0377-9017, Document, MathReview, ZentralBlatt
Referenced by:: §14.17(iv).
Encodings:: BibTeX

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G. C. Donovan, J. S. Geronimo, and D. P. Hardin (1999) Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets. SIAM J. Math. Anal. 30 (5), pp. 1029–1056.

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External Links:: ISSN 0036-1410, Document, MathReview (Kathi Karima Selig), ZentralBlatt
Referenced by:: §16.4(iii).
Encodings:: BibTeX

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T. M. Dunster (2001c) Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions. SIAM J. Math. Anal. 32 (5), pp. 987–1013.

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External Links:: ISSN 0036-1410, Document, MathReview (Hasan Taşeli), ZentralBlatt
Referenced by:: §10.49(ii), §18.34(iii).
Encodings:: BibTeX

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26: Bibliography O

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A. B. Olde Daalhuis (1998c) On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function. Methods Appl. Anal. 5 (4), pp. 425–438.

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External Links:: ISSN 1073-2772, Pdf, MathReview (Éric Delabaere), ZentralBlatt
Referenced by:: §8.12.
Encodings:: BibTeX

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T. Oliveira e Silva (2006) Computing

\pi(x)

: The combinatorial method. Revista do DETUA 4 (6), pp. 759–768.

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Notes:: Online fulltext contains postpublication annotations.
External Links:: FullText
Referenced by:: §27.18.
Encodings:: BibTeX

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F. W. J. Olver (1974) Error bounds for stationary phase approximations. SIAM J. Math. Anal. 5 (1), pp. 19–29.

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Notes:: See also Olver (1997b)
External Links:: Document, MathReview (L. Berg), ZentralBlatt
Referenced by:: §2.3(iv).
Encodings:: BibTeX

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F. W. J. Olver (1991a) Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral. SIAM J. Math. Anal. 22 (5), pp. 1460–1474.

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External Links:: ISSN 0036-1410, Document, MathReview (Hans-Jürgen Glaeske), ZentralBlatt
Referenced by:: §2.11(iii), §2.11(iii), §8.11(i), §8.20(i).
Encodings:: BibTeX

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F. W. J. Olver (1995) 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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External Links:: ISSN 0035-8975, MathReview (Richard B. Paris), ZentralBlatt
Referenced by:: §5.11(iii).
Encodings:: BibTeX

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27: 1.2 Elementary Algebra

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1.2.40

\left\langle\mathbf{u},\mathbf{v}\right\rangle=\sum_{i=1}^{n}u_{i}\overline{v_% {i}}={\mathbf{v}}^{{\rm H}}\mathbf{u}.

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Defines:: $\left\langle\NVar{\mathbf{u}},\NVar{\mathbf{v}}\right\rangle$ : inner product over vectors
Symbols:: ${\NVar{\mathbf{A}}}^{{\rm H}}$ : Hermitian conjugate of matrix, $\overline{\NVar{z}}$ : complex conjugate, $n$ : nonnegative integer, $\mathbf{v}$ : column vector and $\mathbf{u}$ : column vector
Referenced by:: §1.18(i), §1.2(v)
Permalink:: http://dlmf.nist.gov/1.2.E40
Encodings:: pMML, png, TeX
See also:: Annotations for §1.2(v), §1.2(v), §1.2 and Ch.1

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1.2.41

\left\langle\mathbf{u},\mathbf{v}\right\rangle=\overline{\left\langle\mathbf{v% },\mathbf{u}\right\rangle},

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Symbols:: $\overline{\NVar{z}}$ : complex conjugate, $\left\langle\NVar{\mathbf{u}},\NVar{\mathbf{v}}\right\rangle$ : inner product over vectors, $\mathbf{v}$ : column vector and $\mathbf{u}$ : column vector
Permalink:: http://dlmf.nist.gov/1.2.E41
Encodings:: pMML, png, TeX
See also:: Annotations for §1.2(v), §1.2(v), §1.2 and Ch.1

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1.2.42

\left\langle\alpha\mathbf{u},\beta\mathbf{v}\right\rangle=\alpha\overline{% \beta}\left\langle\mathbf{u},\mathbf{v}\right\rangle,

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Symbols:: $\overline{\NVar{z}}$ : complex conjugate, $\left\langle\NVar{\mathbf{u}},\NVar{\mathbf{v}}\right\rangle$ : inner product over vectors, $\mathbf{v}$ : column vector and $\mathbf{u}$ : column vector
Referenced by:: §1.2(v)
Permalink:: http://dlmf.nist.gov/1.2.E42
Encodings:: pMML, png, TeX
See also:: Annotations for §1.2(v), §1.2(v), §1.2 and Ch.1

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1.2.43

\left\langle\mathbf{v},\mathbf{v}\right\rangle=0,

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Symbols:: $\left\langle\NVar{\mathbf{u}},\NVar{\mathbf{v}}\right\rangle$ : inner product over vectors and $\mathbf{v}$ : column vector
Permalink:: http://dlmf.nist.gov/1.2.E43
Encodings:: pMML, png, TeX
See also:: Annotations for §1.2(v), §1.2(v), §1.2 and Ch.1

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1.2.44

\left\langle\mathbf{u},\mathbf{v}\right\rangle=0.

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Symbols:: $\left\langle\NVar{\mathbf{u}},\NVar{\mathbf{v}}\right\rangle$ : inner product over vectors, $\mathbf{v}$ : column vector and $\mathbf{u}$ : column vector
Permalink:: http://dlmf.nist.gov/1.2.E44
Encodings:: pMML, png, TeX
See also:: Annotations for §1.2(v), §1.2(v), §1.2 and Ch.1

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28: Bibliography W

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E. Wagner (1986) Asymptotische Darstellungen der hypergeometrischen Funktion für große Parameter unterschiedlicher Größenordnung. Z. Anal. Anwendungen 5 (3), pp. 265–276 (German).

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External Links:: ISSN 0232-2064, MathReview (R. P. Soni), ZentralBlatt
Referenced by:: §15.12(iii).
Encodings:: BibTeX

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Z. Wang and R. Wong (2006) Uniform asymptotics of the Stieltjes-Wigert polynomials via the Riemann-Hilbert approach. J. Math. Pures Appl. (9) 85 (5), pp. 698–718.

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External Links:: ISSN 0021-7824, Document, MathReview (Rabah Khaldi), ZentralBlatt
Referenced by:: §18.29.
Encodings:: BibTeX

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J. V. Wehausen and E. V. Laitone (1960) Surface Waves. In Handbuch der Physik, Vol. 9, Part 3, pp. 446–778.

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External Links:: Online edition, MathReview (F. Ursell), ZentralBlatt
Referenced by:: §11.12.
Encodings:: BibTeX

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M. I. Weinstein and J. B. Keller (1987) Asymptotic behavior of stability regions for Hill’s equation. SIAM J. Appl. Math. 47 (5), pp. 941–958.

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External Links:: ISSN 0036-1399, Document, MathReview (Ekkehard Wagenführer), ZentralBlatt
Referenced by:: §28.29(iii).
Encodings:: BibTeX

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E. J. Weniger (1996) Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations. Computers in Physics 10 (5), pp. 496–503.

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External Links:: Document
Referenced by:: §2.11(vi), §2.11(vi).
Encodings:: BibTeX

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29: Richard A. Askey

… ►Over his career his primary research areas were in Special Functions and Orthogonal Polynomials, but also included other topics from Classical Analysis and related areas. … ►

5 Gamma Function

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30: Karl Dilcher

… ►Over the years he authored or coauthored numerous papers on Bernoulli numbers and related topics, and he maintains a large on-line bibliography on the subject. …