The letters he exchanged with Jacobi show that Hermite had discovered some differential equations satisfied by theta-functions and he was using Fourier series to study them.
Ang mga titik siya palitan sa Jacobi ipakita na Hermite had natuklasan ng ilang kaugalian equation nasiyahan sa pamamagitan ng theta-function at siya ay gumagamit ng Fourier series sa pag-aaral ng mga ito.