o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o - - - March 15, 1997 - - O P - S F N E T Volume 4, Number 2 - - ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - Editors: - - Tom H. Koornwinder thk@wins.uva.nl - - Martin Muldoon muldoon@yorku.ca - - - - The Electronic News Net of the SIAM Activity Group - - on Orthogonal Polynomials and Special Functions - - - - Please send contributions to: poly@siam.org - - & address changes to: poly-request@siam.org - - - o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o Topic #12 -------------- OP-SF NET 4.2 ------------- March 15,1997 ~~~~~~~~~~~~~ From: Wolfram Koepf Subject: Compiled Booklist and Electronic Services (This item appeared in The Activity Group's Newsletter, February 1997). Here I give the announced list of books and survey papers that should give a basis for understanding the current trends and needs in OP-SF. Let me say that the given list can be neither complete nor perfect. If somebody feels that an important item is missing, please let me know. The following list should rather be understood as under construction. We will try to put this list on OP-SF Web, where it can easily be updated. Electronically, the material could also be more easily organized in various ways. Readers who are interested in classical orthogonal polynomials should probably first look at [Chihara], [NU], [Rainville], [Szego], or [Tricomi]; readers looking for applications in mathematical physics might consider [NU]. [Artin] Artin, E.: "The Gamma Function." Holt, Rinehart and Winston, New York, 1964. [Askey1] Askey, R. A. (Ed.): "Theory and Application of Special Functions". Proceedings of an advanced seminar sponsored by the Mathematics Research Center, University of Wisconsin-Madison, March 21-April 2, 1975. Academic Press, New York, 1975. [Askey2] Askey, R. A. (Ed.): "Orthogonal Polynomials and Special Functions." Regional Conference Series in Applied Mathematics 21, SIAM, Philadelphia, 1975. [AKS] Askey, R. A., Koornwinder, T. H. and Schempp, W. (Eds.): "Special Functions: Group Theoretical Aspects and Applications." Mathematics and Its Applications, Vol. 18. Reidel, Dordrecht-Boston-Lancaster, 1984. [AW3] Askey, R. A. and Wilson, J.: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Memoirs Amer. Math. Soc. 319, Providence, Rhode Island, 1985. [Bailey] Bailey, W. N.: "Generalized Hypergeometric Series". Cambridge University Press, England, 1935; reprinted 1964 by Stechert-Hafner Service Agency, New York-London. [Chihara] Chihara, T. S.: "An Introduction to Orthogonal Polynomials." Gordon and Breach Publ., New York, 1978. [Freud] Freud, G.: "Orthogonale Polynome". Birkhauser, Basel, 1969; English translation, Pergamon Press, Oxford, 1971. [GR] Gasper, G. and Rahman, M.: "Basic Hypergeometric Series." Encyclopedia of Mathematics and Its Applications, Vol. 34. Cambridge University Press, 1990. [Geronimus1] Geronimus, Ya. L.: "Polynomials Orthogonal on a Circle and Interval." International Series of Monographs on Pure and Applied Mathematics, Vol. 18. Pergamon Press, Oxford-London-New York-Paris, 1961. [Geronimus2] Geronimus, Ya. L.: Appendix to the Russian translation of Szego's book "Orthogonal Polynomials." Staatsverlag fur physikalisch-mathematische Literatur, Moskau, 1962. [Henrici1] Henrici, P.: "Applied and Computational Complex Analysis, Vol. 1: Power Series, Integration, Conformal Mapping, Location of Zeros." John Wiley & Sons, New York, 1974. [Henrici2] Henrici, P.: "Applied and Computational Complex Analysis, Vol. 2: Special Functions, Integral Transforms, Asymptotics, Continued Fractions." John Wiley & Sons, New York, 1977. [Hua] Hua, L.K.: "Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains." Translations of Mathematical Monographs, Vol. 6, Amer. Math. Soc., Providence, Rhode Island, 1963. [Lebedev] Lebedev, N. N.: "Special Functions and their Applications." Translated and edited by Richard A. Silverman. Dover Publications, New York, 1972. [LW] Lorentzen, L. and Waadeland, H.: "Continued Fractions with Applications." Studies in Computational Mathematics, Vol. 3. North-Holland, Amsterdam, 1992. [Miller1] Miller, W., Jr.: "Lie Theory and Special Functions." Academic Press, New York, 1968. [Miller2] Miller, W., Jr.: "Symmetry and Separation of Variables." Encyclopedia of Mathematics and Its Applications, Vol. 4. Addison-Wesley, Reading, Massachusetts, 1977. [Nevai1] Nevai, P. G.: "Orthogonal Polynomials." Memoirs Amer. Math. Soc., Vol. 213, Providence, Rhode Island, 1979. [Nevai2] Nevai, P. (Ed.): "Orthogonal Polynomials: Theory and Practice." Proceedings of the NATO Advanced Study Institute on Orthogonal Polynomials and Their Applications, Colombus, Ohio, U.S.A., May 22-June 3, 1989, Kluwer Academic Publ., Dordrecht-Boston-London, 1990. [NU] Nikiforov, A. F. and Uvarov, V. B.: "Special Functions of Mathematical Physics". Translated from the Russian by R. P. Boas, Birkhauser, Basel, 1988. [NSU] Nikiforov, A. F., Suslov, S. K. and Uvarov, V. B.: "Classical Orthogonal Polynomials of a Discrete Variable." Springer-Verlag, Berlin-Heidelberg-New York, 1991. [NS] Nikishin, E. M. and Sorokin, V. N.: "Rational Approximations and Orthogonality." Translations of Mathematical Monographs 92, Amer. Math. Soc., Providence, Rhode Island, 1991. [Olver] Olver, F. W. J.: "Asymptotics and Special Functions." Academic Press, New York, 1974. (reprinted A. K. Peters, 1997) [Perron] Perron, O.: "Die Lehre von den Kettenbruchen." Teubner, Leipzig, 1913; second edition, Chelsea, New York, 1950. [PWZ] Petkovvsek, M., Wilf, H. S. and Zeilberger, D.: "A=B." A. K. Peters, Wellesley, 1996. [Rainville] Rainville, E. D.: "Special Functions". The MacMillan Co., New York, 1960. [Richards] Richards, D. St. P. (Ed.): "Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications." Proceedings of an AMS special session, March 22-23, 1991 in Tampa, FL, USA. Contemporary Mathematics 138, Amer. Math. Soc., Providence, Rhode Island, 1992. [Shohat] Shohat, J. A. and Tamarkin, J. D. : "The Problem of Moments." Amer. Math. Soc., Providence, Rhode Island, 1963. [Szego] Szego, G.: "Orthogonal Polynomials." Amer. Math. Soc. Coll. Publ., Vol. 23, New York, 1939; 4th Edition, 1975. [ST] Stahl, H. and Totik, V.: "General Orthogonal Polynomials." Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge, 1992. [Talman] Talman, J.: "Special Functions: a Group Theoretic Approach." W. A. Benjamin, New York, 1968. [Temme] Temme, N. M.: "Special Functions. An Introduction to the Classical Functions of Mathematical Physics." John Wiley & Sons Inc., New York, 1996. [Tricomi] Tricomi, F. G.: "Vorlesungen uber Orthogonalreihen." Grundlehren der Mathematischen Wissenschaften 76, Springer-Verlag, Berlin-Gottingen-Heidelberg, 1955. [VanAssche] Van Assche, W.: "Asymptotics for Orthogonal Polynomials." Lecture Notes Math. 1265, Springer, Berlin-Heidelberg-New York, 1987. [Vilenkin1] Vilenkin, N. Ya.: "Special Functions and the Theory of Group Representations." Translations of Mathematical Monographs 22, Amer. Math. Soc., Providence, Rhode Island, 1968. [Vilenkin2] Vilenkin, N. Ya., and Klimyk, A. U.: "Representation of Lie Groups and Special Functions, Vols. 1-3, and "Recent Advances", Kluwer Academic Publ., Dordrecht-Boston-London, 1992-1995. [Wall] Wall, H. S.: "Analytic Theory of Continued Fractions." Chelsea, Bronx, NY, 1973. The following are handbooks and other reference manuals for orthogonal polynomials and special functions. [AS] Abramowitz, M. and Stegun, I. A.: "Handbook of Mathematical Functions." Dover Publ., New York, 1964. [Erdelyi1] Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.: "Higher Transcendental Functions, Vols. 1-3." McGraw-Hill, New York, 1953-1955. [Erdelyi1] Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.: "Tables of Integral Transforms, Vols. 1-2." McGraw-Hill, New York, 1954. [GR] Gradshteyn, I. S. and Ryzhik, I. M.: "Table of Integrals, Series, and Products." Printed and CD-ROM Version. Academic Press, San Diego, California, 1996. [Han] Hansen, E. R.: "A Table of Series and Products." Prentice-Hall, Englewood Cliffs, NJ, 1975. [Swarttouw] Koekoek, R. and Swarttouw, R. F.: "The Askey-scheme of hypergeometric orthogonal polynomials and its q analogue." Report 94-05, Technische Universiteit Delft, Faculty of Technical Mathematics and Informatics, Delft, 1994. Electronic version: http://www.can.nl/~renes/index.html [MOS] Magnus, W., Oberhettinger, F. and Soni, R. P.: "Formulas and Theorems for the Special Functions of Mathematical Physics". Springer, Berlin-Heidelberg-New York, 1966. [PBM] Prudnikov, A.P., Brychkov, Yu.A. and Marichev, O.I.: "Integrals and Series, Vols.1-3." Gordon and Breach Publ., New York, 1989-1990. Electronic Services Here is a list of electronic services and WWW sites which are of interest to the members of our Activity Group. [SIAM OPSF] http://www.math.yorku.ca/Who/Faculty/Muldoon/siamopsf SIAM Activity Group on Orthogonal Polynomials and Special Functions. [Addresses] http://www.math.yorku.ca/Who/Faculty/Muldoon/siamopsf/WWWaddresses.html Martin Muldoon and Tom H. Koornwinder: A collection of electronic services relevant for OPSF [OPSF] ftp://unvie6.un.or.at/siam/ Hans Haubold: OPSF ftp site [aboutMathSciNet] http://www.ams.org/msnhtml/about_mathsci.html or http://ams.mathematik.uni-bielefeld.de/about_mathsci.html Mathematical Reviews: about MathSciNet [MathSciNet] http://www.ams.org/msnhtml/mathscinet or http://ams.mathematik.uni-bielefeld.de/mathscinet Mathematical Reviews: MathSciNet [MR] http://www.ams.org/committee/publications/author-lookup.html Mathematical Reviews: Author Lookup [Zentralblatt] http://www.emis.de/cgi-bin/MATH Zentralblatt fur Mathematik: MATH Database 1931-1996 on-line [AMSPPS] http://www.ams.org/preprints AMS: Preprint Server [netlib] http://www.netlib.org Netlib: collection of mathematical software, papers, and databases [CPC] http://www.cpc.cs.qub.ac.uk/cpc Elsevier: The CPC International Program Library [AWS] http://www.can.nl/~renes/index.html Rene Swarttouw: Electronic version of the Askey-Wilson scheme report. [Swarttouw] http://www.can.nl/~demo/CAOP/CAOP.html Rene Swarttouw: An interactive on-line version of the Askey-Wilson scheme, using Koepf's Maple implementations of Zeilberger's algorithm [OMI] http://www.integrals.com Wolfram Research: On-line Mathematica Integrator [ISC] http://www.cecm.sfu.ca/projects/ISC CECM: Inverse Symbolic Calculator [IS] http://netlib.att.com/math/sloane/doc/eistop.html N. J. A. Sloane: Integer Sequences [TI] http://http.cs.berkeley.edu/~fateman/htest.html Richard Fateman: Table of Integrals Look Up [FMC] http://www.mathsoft.com/cgi-shl/constant.bat Steven Finch: Favorite Mathematical Constants [RNC] http://www.cecm.sfu.ca/organics/papers/bailey David H. Bailey and Simon Plouffe: Recognizing Numerical Constants [Numbers] http://archives.math.utk.edu/subjects/numbers.html Mathematics Archives: Numbers [NESF] http://math.nist.gov/nesf Daniel Lozier: Numerical Evaluation of Special Functions Wolfram Koepf