TY - JOUR TI - The series representations for the J and H functions applied in the heat-diffusion equation AU - Yang Xiao-Jun AU - Fan Yu-Rong JN - Thermal Science PY - 2021 VL - 25 IS - 6 SP - 4631 EP - 4642 PT - Article AB - In this article the theory of the supertrigonometric and superhyperbolic functions associated with the J and H functions are proposed for the first time. The series representation for the heat-diffusion equations are also given by using the J and H functions. The results are efficient and accurate for the description for the solutions of the PDE in mathematical physics.