The Appell–Humbert theorem is a result in the theory of complex numbers and multidimensional analysis. It relates to the behavior of certain classes of functions, particularly those that are harmonic or analytic. The theorem states conditions for when a function can be expressed as a series of its values on a certain domain.
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The Appell–Humbert theorem classifies holomorphic line bundles on a complex torus by a Riemann form together with a compatible semicharacter of its lattice.