Yes — many powerful special functions are underutilized in applied mathematics and physics. Beyond the classical Bessel, Legendre, and hypergeometric families, functions such as the Fox H-function, Kampé de Fériet function, and Srivastava–Daoust functions can elegantly describe multivariable dynamics, anomalous diffusion, and fractional processes. They remain overlooked mainly due to their complex definitions, the lack of ready-to-use computational tools in common libraries (e.g., MATLAB, SciPy), and limited exposure in standard curricula. As modern research increasingly embraces fractional calculus, complex networks, and non-Gaussian models, these functions are poised to become as central in the 21st century as Bessel and Legendre were in the past (see Mathai & Haubold, Special Functions for Applied Scientists, 2008).

several special functions are notably underutilized in math.and phys.despite their potential to solve complex problems more elegantly or efficiently, like : Lerch Transcendent fun. useful for modeling complex statistical distributions and calculating non-standard integrals but its computational complexity and difficulty in practical application without specialized tools or not included in standard statistical curricula or require advanced algorithms not readily available in common software like R or python.

In fact, related to this important question I want to ask how one can determine if a space of functions is relevant or not to model physic problems?

Is it not more a problem of experimental physics?