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