meromorphic function
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11: 13.2 Definitions and Basic Properties
12: 23.15 Definitions
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βΊA modular function
is a function of that is meromorphic in the half-plane , and has the property that for all , or for all belonging to a subgroup of SL,
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13: 25.15 Dirichlet -functions
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βΊThe notation was introduced by Dirichlet (1837) for the meromorphic continuation of the function defined by the series
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14: 29.12 Definitions
15: 4.14 Definitions and Periodicity
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βΊThe functions
, , , and are meromorphic, and the locations of their zeros and poles follow from (4.14.4) to (4.14.7).
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16: 8.2 Definitions and Basic Properties
17: 22.2 Definitions
§22.2 Definitions
… βΊEach is meromorphic in for fixed , with simple poles and simple zeros, and each is meromorphic in for fixed . … … βΊThe Jacobian functions are related in the following way. … βΊIn terms of Neville’s theta functions (§20.1) …18: 3.5 Quadrature
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βΊwhich depends on function values computed previously.
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βΊ