Most cited papers in Mathematical functions and polynomials
What are the most cited papers in Mathematical functions and polynomials?
The most cited paper in Mathematical functions and polynomials is "On certain integrals of Lipschitz-Hankel type involving products of bessel functions" (G. Eason, Ben Noble, Ian Naismith Sneddon, 1955), with 4,401 citations. Next come "Smoothing noisy data with spline functions" (3,416) and "On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals" (2,009).
Showing 50 of 100 papers. Every paper with more than 372 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | On certain integrals of Lipschitz-Hankel type involving products of bessel functions G. Eason, Ben Noble, Ian Naismith Sneddon · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences | 19 Apr 1955 | 4,401 |
| 2 | Smoothing noisy data with spline functions Peter G. Craven, Grace Wahba · Numerische Mathematik | Dec 1978 | 3,416 |
| 3 | On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals John H. Halton · Numerische Mathematik | Dec 1960 | 2,009 |
| 4 | Toeplitz Forms and Their Applications Ulf Grenander, Gábor Szegő, Mark Kac · Physics Today | Oct 1958 | 1,875 |
| 5 | 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 |
| 6 | Generalized discrete variable approximation in quantum mechanics J. C. Light, Ian P. Hamilton, James Lill · The Journal of Chemical Physics | Feb 1985 | 1,750 |
| 7 | A new algorithm for adaptive multidimensional integration G. Peter Lepage · Journal of Computational Physics | May 1978 | 1,677 |
| 8 | A ‘missing’ family of classical orthogonal polynomials Luc Vinet, Alexei S. Zhedanov · Journal of Physics A Mathematical and Theoretical | 31 Jan 2011 | 1,645 |
| 9 | On orthogonal polynomials P. Túrán · Analysis Mathematica | Dec 1975 | 1,624 |
| 10 | A Test of Goodness of Fit T. W. Anderson, Donald A. Darling · Journal of the American Statistical Association | Dec 1954 | 1,479 |
| 11 | A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION M. Rosenblatt · Proceedings of the National Academy of Sciences | 1956 | 1,406 |
| 12 | Splines minimizing rotation-invariant semi-norms in Sobolev spaces Jean Duchon · Lecture notes in mathematics | 1977 | 1,394 |
| 13 | Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase Karl Vogel, H. Risken · Physical Review A | Sep 1989 | 1,328 |
| 14 | Some results on Tchebycheffian spline functions George Kimeldorf, Grace Wahba · Journal of Mathematical Analysis and Applications | 1971 | 1,266 |
| 15 | Interpolation of scattered data: Distance matrices and conditionally positive definite functions Charles A. Micchelli · Constructive Approximation | Dec 1986 | 1,245 |
| 16 | Continuous and Discrete Wavelet Transforms Christopher E. Heil, David F. Walnut · SIAM Review | Dec 1989 | 1,218 |
| 17 | HARMONIC POLYLOGARITHMS Ettore Remiddi, J. A. M. Vermaseren · International Journal of Modern Physics A | 20 Feb 2000 | 1,159 |
| 18 | Computing the distribution of quadratic forms in normal variables J. P. Imhof · Biometrika | 1961 | 1,156 |
| 19 | Non‐linear Transformations of Divergent and Slowly Convergent Sequences Daniel N. Shanks · Studies in Applied Mathematics | Apr 1955 | 1,098 |
| 20 | The uncertainty principle: A mathematical survey Gerald B. Folland, Alladi Sitaram · Journal of Fourier Analysis and Applications | May 1997 | 1,000 |
| 21 | Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities Mehmet Zeki Sarıkaya, Erhan Set, Hatice Yaldız et al. · Mathematical and Computer Modelling | 6 Jan 2012 | 936 |
| 22 | Numerical integration using sparse grids Thomas V. Gerstner, Michael Griebel · Numerical Algorithms | 1998 | 930 |
| 23 | Singularity Analysis of Generating Functions Philippe Flajolet, Andrew M. Odlyzko · SIAM Journal on Discrete Mathematics | May 1990 | 860 |
| 24 | Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory Percy A. Deift, T. Kriecherbauer, K. T-R McLaughlin et al. · Communications on Pure and Applied Mathematics | Nov 1999 | 852 |
| 25 | Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula Sever S Dragomir, Ravi P. Agarwal · Applied Mathematics Letters | Sep 1998 | 849 |
| 26 | On the Weierstrass-Mandelbrot fractal function Michael Victor Berry, Z. V. Lewis, John Frederick Nye · Proceedings of the Royal Society of London A Mathematical and Physical Sciences | 24 Apr 1980 | 813 |
| 27 | Classical Orthogonal Polynomials of a Discrete Variable Arnold F. Nikiforov, Vasilii B. Uvarov, Sergeĭ K. Suslov | 1991 | 789 |
| 28 | New approach to a generalized fractional integral Udita N. Katugampola · Applied Mathematics and Computation | 15 Apr 2011 | 762 |
| 29 | Optimal Order of One-Point and Multipoint Iteration H. T. Kung, Joseph F. Traub · Journal of the ACM | Oct 1974 | 758 |
| 30 | A generalized discrepancy and quadrature error bound Fred J. Hickernell · Mathematics of Computation | 1998 | 728 |
| 31 | Applications ofB-splines in atomic and molecular physics H. Bachau, E. Cormier, Piero Decleva et al. · Reports on Progress in Physics | 20 Nov 2001 | 702 |
| 32 | SPECIAL FUNCTIONS (Encyclopedia of Mathematics and its Applications 71) Frits Beukers · Bulletin of the London Mathematical Society | 2001 | 688 |
| 33 | Numerical inversion of the laplace transform: a survey and comparison of methods Brian Davies, Brian Martin · Journal of Computational Physics | Oct 1979 | 680 |
| 34 | An algebra of pseudo‐differential operators Joseph John Kohn, Louis Nirenberg · Communications on Pure and Applied Mathematics | Feb 1965 | 669 |
| 35 | Summation by Parts for Finite Difference Approximations for d/dx Bo Strand · Journal of Computational Physics | 1994 | 664 |
| 36 | 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 |
| 37 | Is Gauss Quadrature Better than Clenshaw–Curtis? Lloyd N. Trefethen · SIAM Review | 2008 | 646 |
| 38 | An Introduction to Orthogonal Polynomials M. Foupouagnigni · Tutorials, schools, and workshops in the mathematical sciences | 2020 | 637 |
| 39 | Orthogonal polynomials T. W. Körner, Terence Tao · Cambridge University Press eBooks | 19 May 2022 | 612 |
| 40 | The Fourier integral and its applications E. Folke Bolinder · Proceedings of the IEEE | 1963 | 607 |
| 41 | Strong asymptotics of orthogonal polynomials with respect to exponential weights Percy A. Deift, Thomas Kriecherbauer, K. T‐R McLaughlin et al. · Communications on Pure and Applied Mathematics | 12 Oct 1999 | 605 |
| 42 | Orthogonal Polynomials Albert L. Rabenstein · Elsevier eBooks | 1972 | 601 |
| 43 | A Review of Definitions for Fractional Derivatives and Integral Edmundo Capelas de Oliveira, J. A. Tenreiro Machado · Mathematical Problems in Engineering | 2014 | 581 |
| 44 | The Exponentially Convergent Trapezoidal Rule Lloyd N. Trefethen, J. A. C. Weideman · SIAM Review | 2014 | 569 |
| 45 | ADDENDUM: NEW INTERPRETATION OF HOMOTOPY PERTURBATION METHOD Ji‐Huan He · International Journal of Modern Physics B | 20 Jul 2006 | 550 |
| 46 | The spectrum of Hill's equation Henry P. McKean, Pierre van Moerbeke · Inventiones mathematicae | Oct 1975 | 546 |
| 47 | Monte Carlo theory and practice F. James · Reports on Progress in Physics | Sep 1980 | 545 |
| 48 | An extension of the method of steepest descents Clive R. Chester, Bernard Friedman, Fritz Joseph Ursell · Mathematical Proceedings of the Cambridge Philosophical Society | Jul 1957 | 539 |
| 49 | What is a fractional derivative? Manuel Duarte Ortigueira, J. A. Tenreiro Machado · Journal of Computational Physics | 22 Jul 2014 | 522 |
| 50 | A Unified Framework for Numerically Inverting Laplace Transforms Joseph Abate, Ward Whitt · INFORMS journal on computing | Nov 2006 | 510 |
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.