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Topic: Special functions

	List of mathematical functions - Wikipedia, the free encyclopedia
		A modern, abstract point of view contrasts large function spaces, which are infinite-dimensional and within which most functions are 'anonymous', with special functions picked out by properties such as symmetry, or relationship to harmonic analysis and group representations.
		Subadditive function: The value of a sum is less than or equal to the sum of the values of the summands.
		Superadditive function: The value of a sum is greater than or equal to the sum of the values of the summands.
	en.wikipedia.org /wiki/List_of_mathematical_functions (796 words)

	Special functions -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		The high point of the special function theory in the period 1850-1900 was the theory of (Click link for more info and facts about elliptic function) elliptic functions; treatises that were essentially complete, such as that of Tannery and Molk, could be written as handbooks to all the basic identities of the theory.
		For a long time the special functions were in the particular province of (The branches of mathematics that are involved in the study of the physical or biological or sociological world) applied mathematics; applications to the physical sciences and engineering determined the relative importance of functions.
		Almost all aspects of special function theory are reflected there, as well as some new ones, such as came out of the (Click link for more info and facts about monstrous moonshine) monstrous moonshine theory.
	www.absoluteastronomy.com /encyclopedia/s/sp/special_functions.htm (702 words)

	Physics Today April 2001
		Some of these functions were (with one class of exceptions) known to mathematicians in 1964, but they were not well known to scientists, and had rarely been applied in physics.
		Functions of hypergeometric type can be ordered by the behavior of singular points of the differential equations representing them, or by a group-theoretical analysis of their symmetries.
		Of the two Airy functions, Ai is the one that decays towards infinity, while Bi grows; the J Bessel functions are regular at the origin, the Y Bessel functions have a pole or a branch point.
	www.physicstoday.org /pt/vol-54/iss-4/p11.html (1453 words)

	A New Testament for Special Functions?
		Exactly what qualifies a function as special is partly a matter of taste, but the list certainly includes such things as Bessel functions, hypergeometric series, and orthogonal polynomials with names like Legendre, Chebychev, and Hermite.
		Almost any special function is actually part of a family of functions (the constant function 1 is a member of many, many families), but some, such as the gamma function and the Riemann zeta function, stand alone.
		The ubiquity of special functions is due in part to the vast number of mathematical identities they satisfy.
	www.siam.org /siamnews/03-98/function.htm (1534 words)

	Special Functions (Site not responding. Last check: 2007-11-06)
		This is required because some aspects of a special function require the layer in which the player sprite resides.
		Functions that reside on a layer other than the player's layer are discernible by the fact that the "Action Parameters" tab hides the controls relavent to the player when such a function is selected.
		Global functions are optimized to know that they don't have to check the position of the player first; just assume that they can be activated purely based on the state of the input device.
	gamedev.sourceforge.net /Help/MapEdit5.htm (4599 words)

	Special Functions
		Thus, for example, integral representations of functions are valid only when the integral exists, but the functions themselves can usually be defined elsewhere by analytic continuation.
		The zeta function for complex arguments is central to number-theoretical studies of the distribution of primes.
		The Legendre functions, and the functions which give generalizations of other orthogonal polynomials, can be expressed in terms of the hypergeometric function.
	documents.wolfram.com /v4/MainBook/3.2.10.html (1396 words)

	Abstracts for Special Functions in the Digital Age , July 22 - August 2, 2002
		The profits of this interaction for special funtion theory were a new way of systematizing the theory, new conceptual proofs of old results, new results for known special functions, and the introduction of completely new classes of special functions.
		Applications of the interaction between special functions and group theory were made in particular in physics (for instance Clebsch-Gordan coefficients), while conversely physical motivation often led to new examples of this interaction.
		In particular, those special functions that arise as explicit solutions of the partial differential equations of mathematical physics, such as via separation of variables, can be characterized in terms of their transformation properties under the Lie symmetry groups and algebras of the differential equations.
	www.ima.umn.edu /digital-age/abstracts (7682 words)

	Mathematical Methods Special Functions Introduction
		These functions are called elementary because they are treated in detail in introductory algebra, trigonometry, and calculus courses and they are used routinely in a variety of engineering applications.
		In contrast, functions that we are not as familiar with are more difficult to use in applications (at least initially) and sometimes these are referred to as non-elementary functions, special functions, or transcendental functions.
		Also, once we gain a little experience with these special functions, we will no longer be imitated with their use and the non-elementary connotation will no longer be applicable (for example, using Bessel functions is as easy as using sinusoids, once you become comfortable with their use).
	gershwin.ens.fr /vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/math/s8/s8intro/s8intro.html (312 words)

	Working with Special Functions
		Most special functions have simpler forms when given certain specific arguments.
		Most special functions have derivatives that can be expressed in terms of elementary functions or other special functions.
		One feature of working with special functions is that there are a large number of relations between different functions, and these relations can often be used in simplifying expressions.
	documents.wolfram.com /v4/MainBook/3.2.13.html (303 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		As stated in the preface of our book "Computation of Special Functions," the purpose of this book is to share with the reader a set of computer programs (130 in total) which we have developed during the past several years for computing a variety of special mathematical functions.
		LGAMA Evaluate the gamma function or the logarithm of the gamma function.
		ITJYB Evaluate the integral of Bessel functions J0(t) and Y0(t) from 0 to x using polynomial approximations.
	www.esrf.fr /computing/expg/libraries/smf/Header.html (2354 words)

	ipedia.com: List of mathematical functions Article (Site not responding. Last check: 2007-11-06)
		Trigonometric functions: sine, cosine, etc.; used in geometry and to describe periodic phenomena.
		Sigma function: Sums of powerss of divisors of a given natural number.
		Euler's phi function: Number of numbers relatively prime to (and not bigger than) a given one.
	www.ipedia.com /list_of_mathematical_functions.html (487 words)

	FoCM'02: Workshop on Special Functions
		One of the new types of special functions to be included is that arising from canonical integrals with coalescing saddles.
		Although studied previously as independent functions, such integrals are the basis of applications of Thom's catastrophe theory to a wide variety of problems, notably caustic diffraction phenomena in wavefield (optics, quantum mechanics, waterwave,...) and uniform asymptotic analysis.
		Virtually all of the classical special functions of mathematical physics (in one and several variables) arise in this study, and formulas expanding one type of special function as a series in another type emerge as a byproduct.
	staff.science.uva.nl /~thk/FoCM02 (2392 words)

	33: Special functions
		Special functions are just that: specialized functions beyond the familiar trigonometric or exponential functions.
		Functions with an addition formula (F(x+y)=P(F(x),F(y)) P a polynomial) are elliptic functions
		Formal definition of the sine function (via integrals) and derivation of some of its properties.
	www.math.niu.edu /~rusin/known-math/index/33-XX.html (611 words)

	Special Functions
		Special functions automatically get applied to each element in a list.
		knows analytical properties of special functions, such as derivatives.
		in which these functions are divided by complete beta and gamma functions.
	documents.wolfram.com /v5/TheMathematicaBook/AdvancedMathematicsInMathematica/MathematicalFunctions/3.2.10.html (1399 words)

	University of Manitoba - Special Functions Department
		catered functions to the University community and the general public.
		In conjunction to this, the department offers a wide range of services both directly and indirectly in support of these functions.
		Annually, the Special Functions Department handles approximately 4500 reservations ranging from simple, no-charge meeting room bookings to large, complex conferences, and special events.
	www.umanitoba.ca /campus/special_functions (76 words)

	Numerical Evaluation of Special Functions
		Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians.
		The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field.
		Maple and Mathematica (§3.4.3 and §3.4.5) were found to have added considerable support for special functions, and three new libraries (§3.2.1, §3.2.3 and §3.3.3) were included.
	math.nist.gov /mcsd/Reports/2001/nesf (323 words)

	DLMF: DLMF Seminar Series (Site not responding. Last check: 2007-11-06)
		Special Functions of Matrix Argument, and their Applications in the Mathematical and Physical Sciences
		Since their appearance in the mid-1950s, the special functions of matrix argument have been studied intensely because of their ubiquity in the mathematical and physical sciences.
		In this talk I will review the history and development of these special functions, illustrated by analogies with the classical special functions of one variable.
	dlmf.nist.gov /about/Events/announcement.php?id=richards-2001-01 (104 words)

	SIXTH INTERNATIONAL SYMPOSIUM (Site not responding. Last check: 2007-11-06)
		It covers the field of orthogonal polynomials and special functions and their applications in the other areas of mathematics, physics and other sciences.
		This Symposium is a forum for presentation and discussion of all aspects of orthogonal polynomials and special functions, ranging from the fundamental to the applied.
		The aim of the Symposium is to provide a common meeting ground for specialists in orthogonal polynomials, special functions and related topics, such as moment problems, rational approximation, matrix orthogonal polynomials, Sobolev orthogonal polynomials as well as in the rich variety of scientific applications of these objects.
	www.mat.uniroma3.it /opsfa2001 (962 words)

	Workshop on Special Functions, Representation Theory and Applications
		The purpose of the workshop is to discuss the recent developments in special functions and representation theory, and their applications in mathematical physics and computer algebra.
		Volume 14 (2003) of Indagationes Mathematicae, New Series is a special issue with research papers dedicated to Tom Koornwinder (contents of the special issue).
		Workshop on Special Functions, Orthogonal Polynomials, Quantum Groups and Related Topics in Bexbach, Germany, October 18-22, 2003, on the occasion of Dick Askey's 70th birthday.
	staff.science.uva.nl /~jstokman/workshop.html (353 words)

	Amazon.com: Books: Special Functions and Their Applications (Site not responding. Last check: 2007-11-06)
		Lebedev is the quintessential mathematical expert in applying Special Functions to problems in Physics and Engineering, being that he can illustrate all important concepts clearly and umambiguously with carefully prepared diagrams as well as words.
		There are numerous other examples which he worked out for different applications (e.g, Legendre's and Laguerre's functions) invariably after he took pains to delineate the various mathematical properties of the Special Functions utilized to obtain the closed-form solutions.
		He also covers various mathematical functions which may not be as familiar to many engineering practitioners but nonetheless have an important place in applied mathematical analysis.
	www.amazon.com /exec/obidos/tg/detail/-/0486606244?v=glance (1226 words)

	Amazon.ca: Books: Representation of Lie Groups and Special Functions: Recent Advances (Site not responding. Last check: 2007-11-06)
		Here, they deal with the exposition of the main new developments in the contemporary theory of multivariate special functions, bringing together material that has not been presented in monograph form before.
		The theory of orthogonal symmetric polynomials (Jack polynomials, Macdonald's polynomials and others) and multivariate hypergeometric functions associated to symmetric polynomials are treated.
		Also, the theory of Gel'fand hypergeometric functions and the theory of multivariate hypergeometric series associated to Clebsch-Gordan coefficients of the unitary group U(n) is given.
	www.amazon.ca /exec/obidos/ASIN/0792332105 (270 words)

	Society for Special Functions and their Applications
		The Society for Special Functions and their Applications (SSFA) was founded in 1998 with its headquarter at Jaunpur (Uttar Pradesh, India), the seat of the Purvanchal University.
		Later, to facilitate its functioning, the Society was reregistered with head quarter at Lucknow in 1999.
		Special Functions : Selected Topics, Proceeding of First Annual Conference, ed.
	www.ssfa.gq.nu (228 words)

	Special Functions, An Introduction to the Classical Functions of Mathematical Physics (Site not responding. Last check: 2007-11-06)
		Usually we call a function "special" when the function, just as the logarithm, the exponential and trigonometric functions (the elementary transcendental functions), belongs to the toolbox of the applied mathematician, the physicist or engineer.
		This book has been written with students of mathematics, physics and engineering in mind, and also researchers in these areas who meet special functions in their work, and for whom the results are too scattered in the general literature.
		In a separate chapter the stability aspects of recurrence relations for several special functions are discussed.
	www.cwi.nl /~nicot/boek.html (1319 words)

	Software Test Service for Special Functions Proposed
		NISTIR 5916, A Proposed Software Test Service for Special Functions, proposes the development of a software test service at NIST for use in testing the accuracy, or numerical precision, of mathematical software for special functions.
		The service would be useful to anyone who uses special functions in physics or other applications.
		It also would stimulate the interest of applied mathematicians in the computation of special functions as well as the interest of computer scientists in innovative uses of the Internet.
	math.nist.gov /mcsd/highlights/specialfunc.html (118 words)

	Algorithmic Combinatorics
		We are mainly interested in the connection of classical combinatorics, special functions, and computer algebra ("symbolic computation in combinatorics").
		Currently, special emphasis is put on symbolic summation and special function identities.
		The RISC combinatorics group is member of the special research action Numerical and Symbolic Scientific Computing (SFB, sponsored by the Austrian Science Foundation FWF).
	www.risc.uni-linz.ac.at /research/combinat/risc (342 words)

	R: Special Functions of Mathematics (Site not responding. Last check: 2007-11-06)
		Special mathematical functions related to the beta and gamma functions.
		return the first and second derivatives of the logarithm of the gamma function.
		functions are generic: methods can be defined for them individually or via the
	pbil.univ-lyon1.fr /library/base/html/Special.html (148 words)

	FORTRAN Routines for Computation of Special Functions
		In the main programs that calculate a sequence of special functions, we usually set the maximum order or degree to 100 or 250.
		mlgama.for (LGAMA) Evaluate the gamma function or the logarithm of the gamma function.
		mitjyb.for (ITJYB) Evaluate the integral of Bessel functions J0(t) and Y0(t) from 0 to x using polynomial approximations.
	jin.ece.uiuc.edu /routines/routines.html (2278 words)

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