Science Explorer Interactive view Map
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. 14.3% 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%
2.8k
per year above
Top-10% rate
14.3%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+16%
the tick is no change

Which countries lead Mathematical functions and polynomials research?

By volume, India and China publish the most (317 and 310 works in 2022–2025).

By volume, 2022–2025

  1. 1 India 317 works
  2. 2 China 310 works
  3. 3 United States 216 works
  4. 4 Russia 166 works
  5. 5 Türkiye 147 works
  6. 6 Saudi Arabia 120 works
  7. 7 Spain 76 works
  8. 8 Pakistan 69 works
  9. 9 Germany 68 works
  10. 10 Italy 65 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.

India: 20.4%China: 19.9%United States: 13.9%Russia: 10.7%6 others listed: 35.1%20%largest
India317 · 20.4%China310 · 19.9%United States216 · 13.9%Russia166 · 10.7%6 others listed545 · 35.1%

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

Which institutions lead Mathematical functions and polynomials research?

By volume in 2022–2025, University of Kashmir publishes the most Mathematical functions and polynomials research, followed by King Saud University and Lomonosov Moscow State University.

By volume, 2022–2025

  1. 1 University of Kashmir India 21 works
  2. 2 King Saud University Saudi Arabia 18 works
  3. 3 Lomonosov Moscow State University Russia 17 works
  4. 4 Akdeniz University Türkiye 15 works
  5. 5 Aligarh Muslim University India 14 works
  6. 6 Düzce Üniversitesi Türkiye 13 works
  7. 7 York University Canada 13 works
  8. 8 Russian Academy of Sciences Russia 13 works
  9. 9 COMSATS University Islamabad Pakistan 12 works
  10. 10 University of Belgrade Serbia 11 works

Where is Mathematical functions and polynomials research done?

The largest centres of Mathematical functions and polynomials research in 2022–2025 are Moscow (Russia), Riyadh (Saudi Arabia), Hangzhou (China) and Seoul (South Korea). Among places with at least 20 works in it, it is an unusually large share of all research in Srinagar.

Largest cities, 2022–2025

  1. 1 Moscow Russia 79 works
  2. 2 Riyadh Saudi Arabia 36 works
  3. 3 Hangzhou China 30 works
  4. 4 Seoul South Korea 27 works
  5. 5 Beijing China 26 works
  6. 6 Madrid Spain 25 works
  7. 7 Srinagar India 25 works
  8. 8 Tashkent Uzbekistan 22 works
  9. 9 Shanghai China 21 works
  10. 10 Tokyo Japan 20 works

Where it is the local speciality

  1. SrinagarIN · 24.6 works21×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Mathematical functions and polynomials than the world average.

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, Aligarh Muslim University and Düzce Üniversitesi 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%20%40%mean 20.73%fractional works in this node (log) →share in the world top 10% →COMSATS University Islamabad: 12, 43.2%Aligarh Muslim University: 14, 33.1%Düzce Üniversitesi: 14, 26.4%Akdeniz University: 15, 30.9%York University: 13, 6.8%King Khalid University: 9, 34.0%King Saud University: 18, 13.3%Lomonosov Moscow State University: 17, 8.7%University of Kashmir: 21, 4.4%University of Hassan II Casablanca: 10, 6.5%COMSATS University I…Aligarh Muslim Unive…Akdeniz UniversityDüzce Üniversitesi
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1COMSATS University Islamabad Pakistan 86.543.2%19.2×12 +224.4%
2Aligarh Muslim University India 69.333.1%20.0×14 +68.4%
3Düzce Üniversitesi Türkiye 68.726.4%31.1×14 +192.6%
4Akdeniz University Türkiye 63.530.9%27.1×15 +10.1%
5York University Canada 57.76.8%13.9×13 +226.3%
6King Khalid University Saudi Arabia 57.534.0%9.0×9 -45.3%
7King Saud University Saudi Arabia 52.313.3%7.6×18 -31.4%
8Lomonosov Moscow State University Russia 50.98.7%7.6×17 +70.8%
9University of Kashmir India 50.74.4%54.2×21 -5.5%
10University of Hassan II Casablanca Morocco 50.36.5%14.7×10 +428.6%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Mathematical functions and polynomials research growing?

Output in 2018–2022 was 16% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Mathematical functions and polynomials.

19801990200020102020
grewheldshrank

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

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.