Topic · Advanced Mathematical Identities
Most cited papers in Advanced Mathematical Identities
What are the most cited papers in Advanced Mathematical Identities?
The most cited paper in Advanced Mathematical Identities is "Table of Integrals, Series, and Products" (I. S. Gradshteyn, I.M. RYZHIK, D. F. Hays, 1976), with 4,749 citations. Next come "Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)" (1,767) and "Approximate formulas for some functions of prime numbers" (1,606).
Showing 50 of 100 papers. Every paper with more than 262 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Table of Integrals, Series, and Products I. S. Gradshteyn, I.M. RYZHIK, D. F. Hays · Journal of Lubrication Technology | Jul 1976 | 4,749 |
| 2 | Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) Milton Abramowitz, Irene A. Stegun, David S. Miller · Journal of Applied Mechanics | Mar 1965 | 1,767 |
| 3 | Approximate formulas for some functions of prime numbers J. Barkley Rosser, Lowell Schoenfeld · Illinois Journal of Mathematics | Mar 1962 | 1,606 |
| 4 | HARMONIC POLYLOGARITHMS Ettore Remiddi, J. A. M. Vermaseren · International Journal of Modern Physics A | 20 Feb 2000 | 1,159 |
| 5 | Probabilistic algorithms for sparse polynomials Richard E. Zippel · Lecture notes in computer science | 1979 | 1,134 |
| 6 | Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities George E. Andrews, R. J. Baxter, Peter J. Forrester · Journal of Statistical Physics | May 1984 | 885 |
| 7 | Singularity Analysis of Generating Functions Philippe Flajolet, Andrew M. Odlyzko · SIAM Journal on Discrete Mathematics | May 1990 | 860 |
| 8 | Algorithm 448: number of multiply-restricted partitions Terry Beyer, D. F. Swinehart · Communications of the ACM | Jun 1973 | 775 |
| 9 | Statistical Theory of Superlattices H. A. Bethe · World Scientific series in 20th century physics | Jul 1997 | 744 |
| 10 | Functoriality for the exterior square of GL₄ and the symmetric fourth of GL₂ Henry Kim · Journal of the American Mathematical Society | 30 Oct 2002 | 710 |
| 11 | On the normal concentration of divisors, 2 Helmut Maier, Gérald Tenenbaum · Mathematical Proceedings of the Cambridge Philosophical Society | 6 Jul 2009 | 697 |
| 12 | Values of Zeta Functions and Their Applications Don Bernard Zagier · Birkhäuser Basel eBooks | 1994 | 659 |
| 13 | The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and 𝑞-series Ken Ono · Regional conference series in mathematics | 22 Dec 2003 | 659 |
| 14 | Percolation Theory for Mathematicians. J. M. Hammersley, Harry Kesten · Journal of the Royal Statistical Society Series A (General) | 1984 | 638 |
| 15 | Some combinatorial properties of Jack symmetric functions Richard P. Stanley · Advances in Mathematics | Sep 1989 | 609 |
| 16 | Tables of Higher Functions Jahnke-Emde-Lösch, Friedrich Lösch, A. A. Maradudin · Physics Today | Mar 1961 | 588 |
| 17 | Ramanujan's Notebooks Bruce C. Berndt · Mathematics Magazine | May 1978 | 587 |
| 18 | Permutohedra, Associahedra, and Beyond Alexander Postnikov · International Mathematics Research Notices | 2009 | 565 |
| 19 | 𝑞-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra George E. Andrews · Regional conference series in mathematics | 31 Dec 1986 | 532 |
| 20 | Duality, quotients, and currents Martin Rocek, Erik Verlinde · Nuclear Physics B | Apr 1992 | 530 |
| 21 | Multiple harmonic series Michael E. Hoffman · Pacific Journal of Mathematics | Feb 1992 | 505 |
| 22 | Ramanujan's Lost Notebook: Part II George E. Andrews, Bruce C. Berndt · DIAL (Catholic University of Leuven) | 2009 | 494 |
| 23 | Combinatorial aspects of continued fractions Philippe Flajolet · Discrete Mathematics | 1980 | 493 |
| 24 | Numerical evaluation of multiple polylogarithms Jens Vollinga, Stefan Weinzierl · Computer Physics Communications | 12 Mar 2005 | 464 |
| 25 | Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property Richard P. Stanley · SIAM Journal on Algebraic and Discrete Methods | Jun 1980 | 457 |
| 26 | The Algebra of Multiple Harmonic Series Michael E. Hoffman · Journal of Algebra | Aug 1997 | 455 |
| 27 | Cascades of sigma factors Richard M. Losick, Janice G. Pero · Cell | Sep 1981 | 447 |
| 28 | Zeroes of zeta functions and symmetry Nicholas Katz, Peter Sarnak · Bulletin of the American Mathematical Society | 1999 | 442 |
| 29 | Operators of Basic (or q-) Calculus and Fractional q-Calculus and Their Applications in Geometric Function Theory of Complex Analysis H. M. Srivastava · Iranian Journal of Science and Technology Transactions A Science | 27 Jan 2020 | 439 |
| 30 | Classical orthogonal polynomials George E. Andrews, Richard Askey · Lecture notes in mathematics | 1985 | 427 |
| 31 | Introduction Richard R. Hall · Cambridge University Press eBooks | 10 Oct 1996 | 422 |
| 32 | Errata: Handbook of mathematical functions with formulas, graphs, and mathematical tables (Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1964) by Milton Abramowitz and Irene A. Stegun Jackson B. Lackey, Henry C. Thatcher · Mathematics of Computation | 1977 | 422 |
| 33 | q-Catalan numbers J Fürlinger, Josef Hofbauer · Journal of Combinatorial Theory Series A | Nov 1985 | 419 |
| 34 | An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities Herbert S. Wilf, Doron Zeilberger · Inventiones mathematicae | Dec 1992 | 413 |
| 35 | Integral moments of L-functions J. Brian Conrey, D. W. Farmer, Jonathan P. Keating et al. · Proceedings of the London Mathematical Society | 22 Jun 2005 | 412 |
| 36 | Fundamentals of Stein’s method Nathan Ross · Probability Surveys | 2011 | 410 |
| 37 | A Hecke Algebra of (Z/rZ)Sn and Construction of Its Irreducible Representations S. Ariki, Kazuhiko Koike · Advances in Mathematics | Jul 1994 | 407 |
| 38 | Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals Erik Panzer · Computer Physics Communications | 30 Oct 2014 | 401 |
| 39 | The Curious History of Faà di Bruno's Formula Warren P. Johnson · American Mathematical Monthly | Mar 2002 | 395 |
| 40 | Two poset polytopes Richard P. Stanley · Discrete & Computational Geometry | Mar 1986 | 394 |
| 41 | A generalization of Kodaira-Ramanujam's vanishing theorem Yūjirō Kawamata · Mathematische Annalen | Mar 1982 | 391 |
| 42 | On the Foundations of Combinatorial Theory Gian‐Carlo Rota · Birkhäuser Boston eBooks | 2009 | 387 |
| 43 | Hyperbolic distribution problems and half-integral weight Maass forms William Duke · Inventiones mathematicae | Feb 1988 | 387 |
| 44 | Further Identities of the Rogers-Ramanujan Type Louise J. Slater · Proceedings of the London Mathematical Society | 1952 | 387 |
| 45 | Dyson’s crank of a partition George E. Andrews, Frank G. Garvan · Bulletin of the American Mathematical Society | 1988 | 387 |
| 46 | Two Notes on Notation Donald E. Knuth · American Mathematical Monthly | May 1992 | 383 |
| 47 | On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory Peter Doubilet, Gian‐Carlo Rota, Joël Stein · Studies in Applied Mathematics | Sep 1974 | 376 |
| 48 | On the Number of Reduced Decompositions of Elements of Coxeter Groups Richard P. Stanley · European Journal of Combinatorics | Dec 1984 | 374 |
| 49 | Special values of multiple polylogarithms Jonathan Michael Borwein, David M. Bradley, David Broadhurst et al. · Transactions of the American Mathematical Society | 11 Oct 2000 | 372 |
| 50 | Some Fractional q-Integrals and q-Derivatives W. A. Al‐Salam · Proceedings of the Edinburgh Mathematical Society | Dec 1966 | 369 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.