Wednesday 26 March 2025
Special functions have been a staple of mathematics for centuries, used to describe everything from the properties of atoms to the curves of the universe. Despite their importance, however, they remain a relatively niche area of study – until now.
A new analysis of the Scopus database has revealed the vast network of special function research that exists across various fields of science and engineering. By visualising the relationships between different authors, keywords, and journals, researchers can gain valuable insights into the most active areas of study and identify potential collaborators.
The dataset, comprising over 4,000 documents, includes a wide range of special functions – from Bessel’s to gamma functions, and even some more esoteric ones like the Mittag-Leffler function. The analysis shows that certain functions are more popular than others, with the hypergeometric function emerging as a clear winner.
But what does this mean for researchers? For one, it provides a valuable resource for those looking to enter the field of special function research. By identifying the most active authors and journals in the area, newcomers can get a sense of where to start their own research journey.
The analysis also highlights some surprising trends. Despite their importance, special functions are rarely used in geometric modeling – a field that is crucial for understanding the shape of objects and how they interact with each other. This could be due to the fact that many researchers in this area don’t have the necessary mathematical tools to work with these functions.
On a more positive note, the analysis shows that there is a growing interest in using special functions to model real-world phenomena. From the properties of materials to the behavior of particles, these functions are being used to gain insights into complex systems.
The analysis also highlights some exciting new developments in the field of special function research. The Julia programming language, for example, has a range of packages that allow researchers to easily calculate and manipulate special functions. This could be particularly useful for those working in fields like geometric modeling, where these functions are essential but often difficult to work with.
The visualisations produced by the analysis are also striking. By mapping out the relationships between different authors, keywords, and journals, researchers can see at a glance which areas of study are most connected – and which ones are isolated. This could be particularly useful for identifying potential collaborations and finding new research partners.
Overall, this new analysis provides a fascinating glimpse into the world of special function research.
Cite this article: “Unraveling the World of Special Functions”, The Science Archive, 2025.
Special Functions, Mathematics, Science, Engineering, Analysis, Scopus Database, Bessel’S Function, Gamma Function, Mittag-Leffler Function, Hypergeometric Function, Geometric Modeling
