The function u = x2-y2 is an example for
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it is an algebraic function
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Harmonic function
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u = x² - y² is a harmonic function.
Harmonic function, mathematical function of two variables having the property that its value at any point is equal to the average of its values along any circle around that point, provided the function is defined within the circle. The major importance of harmonic functions in mathematical physics is mainly due to the frequent occurrence of vector fields of the form . Such fields in domains not containing field sources must satisfy the conservation equation, i.e. the Laplace equation, which means that in such domains is a harmonic function.
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