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absolutely convergent analytical continuation Borel's bounded closed region called canonical product cell circle Clearly closed contour Conformal Mapping constant converges uniformly cosec degree not exceeding diverges Doles elliptic function finite number finite order func function of order genus half-plane imolies inequality infinite product inite integer integral function integrand interior isolated essential singularity Jensen's inequality Lemma lies limiting point Liouville's theorem maximum modulus mesh neighbourhood noint number of zeroes ooint oositive number parallelogram point at infinity points congruent poles polos polygon polynomial of degree primitive periods proves the theorem rational function real axis real numbers regular and non-zero residue Riemann's Theorem Similarly sufficient condition sufficiently large tends to zero term transformation uniformly and absolutely uniformly convergent vanish Weierstrass's Weierstrass's Elliptic Function zero of order