| 11. | The latter is the integral occurring in Dirichlet's principle for harmonic functions.
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| 12. | Thus, there is no simple connection between frequency ratios and harmonic function . ]]
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| 13. | The spherical harmonics are derived from the approach of looking for harmonic functions of the form
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| 14. | One important use of these inequalities is to prove existence of harmonic functions with particular properties.
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| 15. | In particular, the ultrahyperbolic equation satisfies an analog of the mean value theorem for harmonic functions
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| 16. | Since the mean of a harmonic function over a circle is its value at the centre.
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| 17. | Since the mean of the normal derivative of a harmonic function over a circle is zero.
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| 18. | Traditionally, harmonic functions are associated with the real and imaginary parts of an analytic function.
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| 19. | The spherical harmonic functions form a complete orthonormal set of functions in the sense of Fourier series.
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| 20. | In fact, something should be written about harmonic functions in the minimal surface article . ..
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