Extensions described by this adjective for functions on graphs can be constructed using random walks started at each vertex that run until they hit the boundary. The real and imaginary parts of a complex analytic function are “conjugates” described by this adjective. Since their average value over a ball is equal to the value at its center, functions described by this adjective satisfy the mean value property. Solutions to Laplace’s equation are described by this adjective. Since the integral of “one over x” from one to infinity diverges, so does a series described by this adjective according to the integral test. For 10 points, the sum of the reciprocals of each positive integer is a divergent series described by what adjective? ■END■
ANSWER: harmonic [accept harmonic series or harmonic function or harmonic conjugates or harmonic extension]
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= Average correct buzz position