Basic properties of incomplete Macdonald function with applications

• Main Authors: Shu, Jian Jun, Shastri, Kunal Krishnaraj
• Other Authors: School of Mechanical and Aerospace Engineering
• Format: Article
• Language: English
• Published: 2023
• Subjects: Mathematics - Functional Analysis; Vibration Tests; Measuring System
• Online Access: https://hdl.handle.net/10356/165724
• Institution: Nanyang Technological University

The incomplete version of the Macdonald function has various appellations in literature and earns a well-deserved reputation of being a computational challenge. This paper ties together the previously disjoint literature and presents the basic properties of the incomplete Macdonald function, such as recurrence and differential relations, series and asymptotic expansions. This paper also shows that the incomplete Macdonald function, as a simple closed-form expression, is a particular solution to a parabolic partial differential equation, which arises naturally in a wide variety of transient and diffusion-related phenomena.