For example, the Dirichlet series for the zeta function converges absolutely when Re " s " > 1, but the zeta function can be extended to a holomorphic function defined on \ mathbf { C } \ setminus \ { 1 \ } & thinsp; with a simple pole at 1.
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"' Juan de Anza House "', also known as "'Anza House "', is small one-story California adobe in San Juan Bautista, California, USA . It was a simple pole and mud brick building that was typical for the Mexican era in California, including in the 1820-1840 time period in which it was built.
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The rear military mast was replaced by a simple pole mast and sea trials in July 1906 showed that the ship could only attain from . " Dupuy de L�me " was placed in reserve after completing her refit in October 1906 and was not recommissioned until September 1908 for service on the Moroccan station.
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Euler noted that if there were only a finite number of primes, then the product on the right would clearly converge, contradicting the divergence of the harmonic series . ( In modern language, we now say that the existence of infinitely many primes is reflected by the fact that the Riemann zeta function has a simple pole at 1 } } .)
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:: : : : : Of course, it's worth noting that 1 / z is continuous and meromorphic on \ mathbb { C }, with a simple pole at 0.1 / z is most certainly a function, although its continuity is partly because in complex analysis, all infinities are identical . 1 / x just seems odd at first if you don't know about functions which have poles.
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