21. All harmonic functions are analytic, i . e . they can be locally expressed as power series. 22. This equation states that hydraulic head is a harmonic function , and has many analogs in other fields. 23. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions . 24. Alternatively, this equation follows from the relation of the spherical harmonic functions with the Wigner D-matrix. 25. These definitions reflect a relationship between martingale theory and potential theory, which is the study of harmonic functions . 26. Fourth, one can use conformal symmetry to extend harmonic functions to harmonic functions on conformally flat Riemannian manifolds. 27. Fourth, one can use conformal symmetry to extend harmonic functions to harmonic functions on conformally flat Riemannian manifolds. 28. The " weak maximum principle " for harmonic functions is a simple consequence of facts from calculus. 29. Matrix elements and the real part of corresponding harmonic functions of cubic operator basis in J = 1 case. 30. That the latter is a Hilbert space at all is a consequence of the mean value theorem for harmonic functions .
