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then the function
: <math>f(z) = \prod_{n=1}^\infty E_{p_n}(z/a_n)</math>
is entire with zeros only at points <math>a_n</math>.<ref name="rudin"/> If a number <math>z_0</math> occurs in the sequence <math>\{a_n\}</math> exactly {{math|''m''}} times, then the function {{math|''f''}} has a zero at <math>z=z_0</math> of multiplicity {{math|''m''}}.
* The sequence <math>\{p_n\}</math> in the statement of the theorem always exists. For example, we could always take <math>p_n=n</math> and have the convergence. Such a sequence is not unique: changing it at finite number of positions, or taking another sequence {{math|''p''′<sub>''n''</sub> ≥ ''p''<sub>''n''</sub>}}, will not break the convergence.
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