## DLMF

 swMATH ID: 4968 Software Authors: Lozier, Daniel W. Description: NIST digital library of mathematical functions. The National Institute of Standards and Technology is preparing a Digital Library of Mathematical Functions (DLMF) to provide useful data about special functions for a wide audience. The initial products will be a published handbook and companion Web site, both scheduled for completion in 2003. More than 50 mathematicians, physicists and computer scientists from around the world are participating in the work. The data to be covered include mathematical formulas, graphs, references, methods of computation, and links to software. Special features of the Web site include 3D interactive graphics and an equation search capability. The information technology tools that are being used are, of necessity, ones that are widely available now, even though better tools are in active development. For example, LaTeX files are being used as the common source for both the handbook and the Web site. This is the technology of choice for presentation of mathematics in print but it is not well suited to equation search, for example, or for input to computer algebra systems. These and other problems, and some partially successful work-arounds, are discussed in this paper and in the companion paper by {it B. R. Miller} and {it A. Youssef} lbrack ibid. 38, 121–136 (2003; Zbl 1019.65002) brack. Homepage: http://dlmf.nist.gov/ Keywords: mathematical formulas; special functions; handbook; digital library of mathematical functions; knowledge management; web site; methods of computation; computer algebra systems Related Software: Mathematica; Matlab; OEIS; Chebfun; GitHub; Maple; OPQ; R; SageMath; mctoolbox; Equator; FastGaussQuadrature; Arb; Julia; LaTeX; Algorithm 644; Wolfram Functions Site; SumTools; gfun; LaTeXML Referenced in: 2,885 Publications
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### Referenced by 3,691 Authors

 33 López, José Luis 29 Baricz, Árpád 28 Paris, Richard Bruce 27 Gaunt, Robert Edward 25 Segura, Javier 24 Chu, Yuming 22 Cohl, Howard Saul 22 Nemes, Gergő 22 Temme, Nico M. 20 Neuman, Edward 19 Gil, Amparo 18 Vignat, Christophe 17 Borwein, Jonathan Michael 17 Qi, Feng 17 Townsend, Alex 16 Fukushima, Toshio 15 Dilcher, Karl 15 Janson, Svante 15 Olver, Sheehan Shakiban 15 Pogány, Tibor K. 15 Zhang, Lun 14 Dai, Dan 14 Frolenkov, Dmitriĭ Andreevich 14 Pagola, Pedro J. 14 Pérez Sinusía, Ester 14 Van Assche, Walter 14 Xu, Shuaixia 13 Boyd, John Philip 13 Choi, Junesang 13 Dixit, Atul 13 González-Santander, Juan Luis 13 Luo, Minjie 13 Zhao, Yuqiu 12 Akemann, Gernot 12 Ishkhanyan, Artur Michaĭlovich 12 Karp, Dmitriĭ Borisovich 12 Sooppy Nisar, Kottakkaran 12 Teschl, Gerald 11 Balkanova, Ol’ga Germanovna 11 Ciaurri, Óscar 11 Deconinck, Bernard 11 Dehesa, Jesús S. 11 Dunster, T. M. 11 Parmar, Rakesh Kumar 11 Wang, Miaokun 11 Wong, Roderick Sue-Chuen 10 Barnett, Alex H. 10 Dominici, Diego Ernesto 10 Ferreira, Chelo 10 Forrester, Peter J. 10 Moll, Victor Hugo 10 Schmidt, Maxie Dion 10 Srivastava, Hari Mohan 10 Toranzo, Irene V. 9 Bothner, Thomas 9 Brauchart, Johann S. 9 Deaño, Alfredo 9 Donninger, Roland 9 Fornberg, Bengt 9 Qiu, Songliang 9 Raina, Ravinder Krishna 9 Schubotz, Moritz 9 Straub, Armin 9 Trogdon, Thomas 9 Varona Malumbres, Juan Luis 9 Volkmer, Hans 9 Wang, Haiyong 9 Yakubovich, Semyon B. 9 Youssef, Abdou S. 8 Agarwal, Praveen 8 Bremer, James C. 8 Bringmann, Kathrin 8 Charlier, Christophe 8 Chen, Le 8 Guo, Bai-Ni 8 Jiang, Shidong 8 Jiu, Lin 8 Kuijlaars, Arno B. J. 8 Lenells, Jonatan 8 Miller, Peter D. 8 O’Neil, Michael 8 Sidi, Avram 8 Singh, Sanjeev-Kumar 8 Womersley, Robert S. 7 Amdeberhan, Tewodros 7 Bailey, David Harold 7 Celeghini, Enrico 7 del Olmo, Mariano A. 7 Galkowski, Jeffrey 7 Greengard, Leslie F. 7 Jankov Maširević, Dragana 7 Kostenko, Aleksey S. 7 Penson, Karol A. 7 Pizzocchero, Livio 7 Ponnusamy, Saminathan 7 Štampach, František 7 Szasz, Robert Zoltan 6 af Klinteberg, Ludvig 6 Area, Iván 6 Berry, Michael Victor ...and 3,591 more Authors
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### Referenced in 516 Serials

 108 Journal of High Energy Physics 100 Journal of Mathematical Analysis and Applications 77 Journal of Mathematical Physics 65 Applied Mathematics and Computation 64 Integral Transforms and Special Functions 48 Journal of Approximation Theory 43 Communications in Mathematical Physics 43 Journal of Computational Physics 40 Journal of Computational and Applied Mathematics 40 The Ramanujan Journal 38 Proceedings of the American Mathematical Society 37 Journal of Physics A: Mathematical and Theoretical 36 Annals of Physics 36 Journal of Statistical Mechanics: Theory and Experiment 31 Journal of Statistical Physics 31 Mathematics of Computation 31 Constructive Approximation 28 Journal of Fluid Mechanics 27 SIAM Journal on Scientific Computing 26 Analysis and Applications (Singapore) 25 Classical and Quantum Gravity 24 Results in Mathematics 24 Journal of Classical Analysis 23 Numerical Algorithms 22 Nonlinearity 22 Journal of Cosmology and Astroparticle Physics 21 Journal of Scientific Computing 21 Advances in Computational Mathematics 20 Nuclear Physics. B 20 SIAM Journal on Applied Mathematics 19 Journal of Differential Equations 19 Numerische Mathematik 18 Physica D 18 Annales Henri Poincaré 17 Journal of Number Theory 17 SIAM Journal on Numerical Analysis 17 Applied and Computational Harmonic Analysis 17 Random Matrices: Theory and Applications 17 Research in Number Theory 16 Statistics & Probability Letters 15 Journal of Functional Analysis 14 Physics Letters. B 14 Wave Motion 14 Advances in Mathematics 14 Studies in Applied Mathematics 14 Mathematical Inequalities & Applications 13 Physics Letters. A 13 Transactions of the American Mathematical Society 13 Stochastic Processes and their Applications 12 Inverse Problems 12 ACM Transactions on Mathematical Software 12 Communications in Statistics. Theory and Methods 12 SIAM Journal on Mathematical Analysis 12 Electronic Journal of Probability 12 Journal of Inequalities and Applications 12 Communications in Nonlinear Science and Numerical Simulation 11 Linear Algebra and its Applications 11 Journal of Nonlinear Science 11 Fractional Calculus & Applied Analysis 11 Integers 11 International Journal of Number Theory 11 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 10 Computer Physics Communications 10 General Relativity and Gravitation 10 Applied Numerical Mathematics 10 Discrete and Continuous Dynamical Systems 10 Advances in Difference Equations 10 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 9 Modern Physics Letters A 9 Journal of Engineering Mathematics 9 Letters in Mathematical Physics 9 Mathematical Methods in the Applied Sciences 9 Journal of Difference Equations and Applications 9 The Journal of Fourier Analysis and Applications 9 Foundations of Computational Mathematics 9 Computational Methods and Function Theory 9 Journal of Mathematical Inequalities 9 Electronic Journal of Statistics 8 Computers & Mathematics with Applications 8 Physica A 8 Integral Equations and Operator Theory 8 Applied Mathematical Modelling 8 Journal of Mathematical Sciences (New York) 8 Journal of Integer Sequences 8 Mathematics in Computer Science 7 American Mathematical Monthly 7 Archive for Rational Mechanics and Analysis 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Journal of Theoretical Probability 7 Aequationes Mathematicae 7 Communications in Partial Differential Equations 7 SIAM Review 7 Turkish Journal of Mathematics 7 Lobachevskii Journal of Mathematics 7 SIAM Journal on Applied Dynamical Systems 7 Mediterranean Journal of Mathematics 7 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 6 International Journal of Modern Physics A 6 Applicable Analysis 6 European Journal of Physics ...and 416 more Serials
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### Referenced in 60 Fields

 892 Special functions (33-XX) 478 Partial differential equations (35-XX) 472 Numerical analysis (65-XX) 377 Quantum theory (81-XX) 349 Probability theory and stochastic processes (60-XX) 298 Number theory (11-XX) 257 Ordinary differential equations (34-XX) 241 Approximations and expansions (41-XX) 187 Real functions (26-XX) 174 Relativity and gravitational theory (83-XX) 166 Harmonic analysis on Euclidean spaces (42-XX) 165 Statistics (62-XX) 159 Statistical mechanics, structure of matter (82-XX) 148 Functions of a complex variable (30-XX) 114 Combinatorics (05-XX) 112 Linear and multilinear algebra; matrix theory (15-XX) 112 Fluid mechanics (76-XX) 97 Integral transforms, operational calculus (44-XX) 90 Computer science (68-XX) 85 Operator theory (47-XX) 84 Dynamical systems and ergodic theory (37-XX) 76 Mechanics of deformable solids (74-XX) 76 Optics, electromagnetic theory (78-XX) 52 Biology and other natural sciences (92-XX) 50 Integral equations (45-XX) 50 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 49 Differential geometry (53-XX) 48 Mechanics of particles and systems (70-XX) 45 Difference and functional equations (39-XX) 45 Global analysis, analysis on manifolds (58-XX) 44 Information and communication theory, circuits (94-XX) 39 Potential theory (31-XX) 35 Functional analysis (46-XX) 31 Sequences, series, summability (40-XX) 26 Systems theory; control (93-XX) 22 Algebraic geometry (14-XX) 22 Classical thermodynamics, heat transfer (80-XX) 21 Operations research, mathematical programming (90-XX) 20 Topological groups, Lie groups (22-XX) 16 Astronomy and astrophysics (85-XX) 14 Convex and discrete geometry (52-XX) 14 Geophysics (86-XX) 13 Nonassociative rings and algebras (17-XX) 12 Several complex variables and analytic spaces (32-XX) 11 Group theory and generalizations (20-XX) 10 Measure and integration (28-XX) 10 Abstract harmonic analysis (43-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 9 Geometry (51-XX) 7 History and biography (01-XX) 6 $$K$$-theory (19-XX) 6 Manifolds and cell complexes (57-XX) 4 Mathematical logic and foundations (03-XX) 4 Associative rings and algebras (16-XX) 3 General and overarching topics; collections (00-XX) 3 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Mathematics education (97-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX)