Science Explorer Back to mapMap
Discussion
Topic · Applied Mathematics

Mathematical functions and polynomials

Mathematical functions and polynomials is a research topic within Applied Mathematics. Science Explorer counts 19k research works in it since 1950. 10.2% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the theory, computation, and applications of orthogonal polynomials. It covers topics such as quadrature methods, approximation, interpolation, asymptotics, numerical stability, matrix valued polynomials, Riemann-Hilbert approach, random matrix theory, and hypergeometric functions.

  • Orthogonal Polynomials
  • Quadrature Methods
  • Approximation
  • Interpolation
  • Asymptotics
  • Numerical Stability
  • Matrix Valued Polynomials
  • Riemann-Hilbert Approach
  • Random Matrix Theory
  • Hypergeometric Functions
Research works
19k
fractional, since 1950
In the world top 10%
2k
per year above
Top-10% rate
10.2%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+12%
the tick is no change
Largest producer
China
21% of the 10 largest, 2022-now
Mathematical functions and polynomials

Which countries lead Mathematical functions and polynomials research?

By volume, China and India publish the most (370 and 354 works in 2022-now).

By volume, 2022-now

  1. 1 China 370 works
  2. 2 India 354 works
  3. 3 United States 267 works
  4. 4 Russia 185 works
  5. 5 Türkiye 159 works
  6. 6 Saudi Arabia 133 works
  7. 7 Spain 84 works
  8. 8 Germany 84 works
  9. 9 France 77 works
  10. 10 Pakistan 74 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 20.7%India: 19.8%United States: 15.0%Russia: 10.4%6 others listed: 34.2%21%largest
China370 · 20.7%India354 · 19.8%United States267 · 15.0%Russia185 · 10.4%6 others listed610 · 34.2%

Shares of the rows listed above, not of the whole node.

Which institutions lead Mathematical functions and polynomials research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Mathematical functions and polynomials research, followed by Centre National de la Recherche Scientifique and University of Kashmir.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 63 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 35 works
  3. 3 University of KashmirIndia 22 works
  4. 4 Lomonosov Moscow State UniversityRussia 20 works
  5. 5 King Saud UniversitySaudi Arabia 19 works
  6. 6 Akdeniz UniversityTürkiye 16 works
  7. 7 Aligarh Muslim UniversityIndia 16 works
  8. 8 York UniversityCanada 15 works
  9. 9 Düzce ÜniversitesiTürkiye 14 works
  10. 10 National Academy of Sciences of UkraineUkraine 14 works

Who are the leading researchers in Mathematical functions and polynomials?

The most-cited researchers publishing on Mathematical functions and polynomials include R. W. L. Jones.

  1. 1 R. W. L. Jones United Kingdom 189k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

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).

Most cited papers
#PaperReleasedCitations
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
All 100 most cited papers, with filters and sorting

Where is Mathematical functions and polynomials research done?

The largest centres of Mathematical functions and polynomials research in 2022-now are Moscow (Russia), Riyadh (Saudi Arabia), Hangzhou (China) and Beijing (China).

Largest cities, 2022-now

  1. 1 MoscowRussia 87 works
  2. 2 RiyadhSaudi Arabia 40 works
  3. 3 HangzhouChina 34 works
  4. 4 BeijingChina 32 works
  5. 5 SeoulSouth Korea 30 works
  6. 6 MadridSpain 27 works
  7. 7 TashkentUzbekistan 26 works
  8. 8 ShanghaiChina 25 works
  9. 9 SrinagarIndia 25 works
  10. 10 TokyoJapan 24 works
See Mathematical functions and polynomials on the map

Where is the best place to study Mathematical functions and polynomials?

Among universities, judged by research, COMSATS University Islamabad, Eastern Mediterranean University and King Saud University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%30%mean 17.84%fractional works in this field (log) →share of work in the world top 10% →COMSATS University I…King Khalid UniversityEastern Mediterranea…King Saud University
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1COMSATS University IslamabadPakistan 78.928.0%21.6×14 +0.5%
2Eastern Mediterranean UniversityCyprus 64.320.8%53.2×9 +48.6%
3King Saud UniversitySaudi Arabia 62.99.1%7.3×19 +234.9%
4King Khalid UniversitySaudi Arabia 62.222.0%9.1×9 +170.7%
5Hangzhou Normal UniversityChina 62.022.4%18.5×12 +217.9%
6Lomonosov Moscow State UniversityRussia 59.37.1%8.8×20 +25.3%
7Düzce ÜniversitesiTürkiye 58.420.3%33.1×14 -22.6%
8King Faisal UniversitySaudi Arabia 56.021.7%11.8×8 +306.5%
9Akdeniz UniversityTürkiye 55.87.1%25.4×16 +48.1%
10Aligarh Muslim UniversityIndia 53.819.9%19.6×16 -33.6%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Mathematical functions and polynomials, country by country

Is Mathematical functions and polynomials research growing?

Output in 2022-2025 was 12% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Mathematical functions and polynomials.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Mathematical functions and polynomials as a percentage of every work published that year, 0.013% in 2024.

still counting0.020%0.040%0.060%Mathematical functions and polynomials0.013% in 202519801990200020102020

Fractional works of Mathematical functions and polynomials over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Mathematical functions and polynomials10.3% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

Discussion

Ask a question or share a note about Mathematical functions and polynomials. Posts are plain text and can be reported.