🤖 AI Summary
Prior bibliometric studies on special functions lack systematic network visualization (e.g., author collaboration, keyword co-occurrence) and interdisciplinary application assessment. Method: This study conducts the first comprehensive, multi-dimensional bibliometric analysis of 4,025 Scopus-indexed mathematical publications (1940–2024) containing “special function,” employing Julia and the Scopus API to construct dynamic collaboration networks and temporal keyword evolution maps; Gephi/GraphPlot and video-based visualization techniques further enable spatiotemporal pattern analysis. Contribution/Results: The work identifies high-impact scholars and underexplored cross-disciplinary domains—particularly geometric modeling—and delivers an interactive visualization platform, pedagogical video tutorials, and a reproducible analytical framework for mathematics education and interdisciplinary research. It empirically reveals the longstanding underutilization of special functions in applied fields such as computer-aided design (CAD) and architecture.
📝 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.