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1: Karl Dilcher

… ► 1954 in Wabern-Harle, Germany) is Professor in the Department of Mathematics and Statistics at Dalhousie University in Halifax, Nova Scotia, Canada. He received his undergraduate education at the Technische Universität Clausthal in Germany. He then did his graduate studies at Queen’s University in Kingston, Ontario, and finished his Ph. …there in 1983 under the supervision of Paulo Ribenboim. … ►In November 2015, Dilcher was named Associate Editor for his chapter.

2: Sidebar 9.SB1: Supernumerary Rainbows

… ►The faint line below the main colored arc is a ‘supernumerary rainbow’, produced by the interference of different sun-rays traversing a raindrop and emerging in the same direction. …Airy invented his function in 1838 precisely to describe this phenomenon more accurately than Young had done in 1800 when pointing out that supernumerary rainbows require the wave theory of light and are impossible to explain with Newton’s picture of light as a stream of independent corpuscles. The house in the picture is Newton’s birthplace. ►Photograph by Dr. Roy Bishop, Physics Department, Acadia University, Nova Scotia, Canada. See Bishop (1981). ©R. L. Bishop.

3: 24 Bernoulli and Euler Polynomials

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4: Roderick S. C. Wong

… ► 1944 in Shanghai, China) joined the City University of Hong Kong in 1994 as Professor and Head of the Department of Mathematics. … ►He is the author of the book Asymptotic Approximations of Integrals, published by Academic Press in 1989 and reprinted by SIAM in its Classics in Applied Mathematics Series in 2001, and of Lecture Notes on Applied Analysis, published by World Scientific in 2010. … ►Wong was elected a Fellow of the Royal Society of Canada in 1993, a Foreign Member of the Academy of Science of Turin, Italy, in 2001, a Chevalier dans l’Ordre National de la Légion d’Honneur in 2004, and a Member of the European Academy of Sciences in 2007. He was recipient of the Killam Research Fellowship from the Canada Council in 1982–1984, and of the Rh Award for Outstanding Contributions to Scholarship and Research from the University of Manitoba in 1984. … ►In November 2015, Wong was named an Associate Editor for Chapters 2 and 18.

5: Stephen M. Watt

… ► 1959 in Montreal, Canada) is Professor of Computer Science in the David R. … ►In November 2015, Watt was named a Senior Associate Editor of the DLMF.

6: Frank W. J. Olver

… ► 1924 in Croydon, U. …degrees in mathematics from the University of London in 1945, 1948, and 1961, respectively. … ►His well-known book, Asymptotics and Special Functions, was reprinted in the AKP Classics Series by AK Peters, Wellesley, Massachusetts, in 1997. … ►In 1992 he retired, and was appointed Professor Emeritus. … ►In 1989 the conference “Asymptotic and Computational Analysis” was held in Winnipeg, Canada, in honor of Olver’s 65th birthday, with Proceedings published by Marcel Dekker in 1990. …

7: Bibliography S

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Instantons in QCD. Rev. Modern Phys. 70 (2), pp. 323–425.

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External Links:

ISSN 0034-6861, Document, MathReview, ZentralBlatt

Referenced by:

§22.19(ii).

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Use of analyticity in the calculation of nonrelativistic scattering amplitudes. Phys. Rev. 167, pp. 1411–1423.

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External Links:

Document, Link

Referenced by:

(18.40.9), §18.40(ii).

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Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity. 4th edition, Springer-Verlag, Berlin.

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Notes:

Volume 7 in Springer Series in Information Sciences.

External Links:

ZentralBlatt

Referenced by:

§27.16, §27.17.

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The Gaussian Function in Calculations of Statistical Mechanics and Quantum Mechanics. In Methods in Computational Physics: Advances in Research and Applications, B. Alder, S. Fernbach, and M. Rotenberg (Eds.), Vol. 2, pp. 1–45.

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Referenced by:

§8.24(i), §8.24(iii).

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Automatic computing methods for special functions. III. The sine, cosine, exponential integrals, and related functions. J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 291–311.

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Notes:

Includes Fortran code, maximum accuracy 18S.

External Links:

MathReview (Martin E. Price), ZentralBlatt

Referenced by:

§6.21(ii).

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8: Publications

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The DLMF Project: A New Initiative in Classical Special Functions, in Special Functions—Proceedings of the International Workshop, Hong Kong, June 21-25, 1999 (C. Dunkl, M. Ismail, R. Wong, eds.), World Scientific, pp. 207–220.

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From 2D to 3D: Numerical Grid Generation and the Visualization of Complex Surfaces, Proceedings of the 7th International Conference on Numerical Grid Generation in Computational Field Simulations, Whistler, British Columbia, Canada, September 25-28, 2000.

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Handbook of Mathematical Functions, in A Century of Excellence in Measurements Standards and Technology (D. R. Lide, ed.), CRC Press, pp. 135–139.

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Roles of Math Search in Mathematics, in Mathematical Knowledge Management, Proceedings of the 5th International Conference on Mathematical Knowledge Management, Lecture Notes in Computer Science, Vol. 4108, Springer-Verlag, 2006.

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Advances in Math Search, Proceedings 6th International Congress on Industrial and Applied Mathematics, Zürich, Switzerland, July 17, 2007.

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9: Bibliography I

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An integral which occurs in statistics. Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.

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External Links:

Document, ZentralBlatt

Referenced by:

§35.3(i), §35.3(ii).

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Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.

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Notes:

From a decimal approximation, find the most likely exact value.

External Links:

Inverse Symbolic Calculator

Referenced by:

3rd item.

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A First Course in the Numerical Analysis of Differential Equations. Cambridge Texts in Applied Mathematics, No. 15, Cambridge University Press, Cambridge.

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ISBN 0-521-55376-8; 0-521-55655-4, MathReview (Luis Verde-Star), ZentralBlatt

Referenced by:

§3.7(i).

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Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.

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ISBN 978-0-521-78201-2; 0-521-78201-5, MathReview Entry, ZentralBlatt

Referenced by:

§1.4(v), Profile Mourad E.H. Ismail, Erratum (V1.0.20) for Chapter 18 Orthogonal Polynomials.

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The Isomonodromic Deformation Method in the Theory of Painlevé Equations. Lecture Notes in Mathematics, Vol. 1191, Springer-Verlag, Berlin.

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External Links:

ISBN 3-540-16483-9, MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§32.11(iv), §32.4(i), Profile Alexander A. Its.

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10: Bibliography N

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Toda equation and its solutions in special functions. J. Phys. Soc. Japan 65 (6), pp. 1589–1597.

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ISSN 0031-9015, Document, MathReview, ZentralBlatt

Referenced by:

§18.38(ii).

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Coulomb Functions for Large Values of the Parameter $\eta$ . Technical report Atomic Energy of Canada Limited, Chalk River, Ontario.

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Notes:

Rep. CRT-526

External Links:

MathReview (A. Erdélyi)

Referenced by:

§33.7.

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Diffraction Effects in Semiclassical Scattering. Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.

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Notes:

Also available electronically through Cambridge Books Online, ISBN 9780511599903.

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ISBN 9780521383189, Document

Referenced by:

§9.16, §9.16.

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Dislocation lines in the hyperbolic umbilic diffraction catastrophe. Proc. Roy. Soc. Lond. Ser. A 462, pp. 2299–2313.

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ISSN 1364-5021, Document, MathReview, ZentralBlatt

Referenced by:

§36.7(iv).

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Dislocation lines in the swallowtail diffraction catastrophe. Proc. Roy. Soc. Lond. Ser. A 463, pp. 343–355.

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External Links:

ISSN 1364-5021, Document, ZentralBlatt

Referenced by:

§36.7(iv).

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