Network visualisations related to special functions based on the Scopus data since 1940

TL;DR

This paper provides the first bibliometric network visualisations of special functions research based on Scopus data since 1940, highlighting publication trends, author collaborations, and topic connections.

Contribution

It introduces novel network visualisations of special functions literature, using bibliometric data to reveal research patterns and connections in mathematics since 1940.

Findings

Special functions are rarely used in geometric modelling.

Visualisations help identify influential authors and popular topics.

Generated images and videos aid teaching and research exploration.

Abstract

Special functions are essential in theoretical and applied mathematics and have various applications in the applied sciences. Mathematicians have studied them for centuries, but there is still no bibliometric analysis that summarises the datasets of publications showing different network visualisations, such as co-author and keyword visualisations, basic keyword statistics and other data analyses. This work appears to be the first attempt to fill this gap by presenting different network visualisations based on 4025 documents with the keyword "special function" in their title, abstract or keywords belonging to the field of mathematics in the Scopus database. We also show that special functions are rarely used in geometric modelling, a mathematical foundation for CAD, industrial design, architecture, and other applied fields, and we discuss how different visualisations for special functions can be generated in the Julia programming language. The generated image and video visualisations can be helpful to academics to see the impact of different authors, to define their new research topics, to see connections or lack thereof between various topics, to find the most popular special functions, or for teaching purposes to show the importance of special functions and links to other topics in modern pure and applied mathematics and other sciences.