Before arriving at Halle, Heine published on partial differential equations and during his first few years teaching at Halle he wrote papers on the theory of heat, summation of series, continued fractions and elliptic functions.
Bago pagdating sa Halle, Heine-publish sa mga bahagi ng equation kaugalian at sa panahon ng kanyang unang ilang taon na pagtuturo at Halle wrote siya sa mga papeles ang mga teorya ng init, pagbubuo ng serye, ang patuloy na fractions at tambilugin function.