of periodic functions
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11: 22.4 Periods, Poles, and Zeros
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§22.4(i) Distribution
►For each Jacobian function, Table 22.4.1 gives its periods in the -plane in the left column, and the position of one of its poles in the second row. … ►Table 22.4.2 displays the periods and zeros of the functions in the -plane in a similar manner to Table 22.4.1. … ► … ►§22.4(iii) Translation by Half or Quarter Periods
…12: 29.10 Lamé Functions with Imaginary Periods
§29.10 Lamé Functions with Imaginary Periods
… ►The first and the fourth functions have period ; the second and the third have period . …13: 20.2 Definitions and Periodic Properties
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§20.2(ii) Periodicity and Quasi-Periodicity
►For fixed , each is an entire function of with period ; is odd in and the others are even. … ►The theta functions are quasi-periodic on the lattice: … ►§20.2(iii) Translation of the Argument by Half-Periods
…14: 23.7 Quarter Periods
§23.7 Quarter Periods
…15: 28.11 Expansions in Series of Mathieu Functions
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►Let be a -periodic function that is analytic in an open doubly-infinite strip that contains the real axis, and be a normal value (§28.7).
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16: 28.12 Definitions and Basic Properties
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28.12.6
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17: 23.2 Definitions and Periodic Properties
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§23.2(iii) Periodicity
… ►Hence is an elliptic function, that is, is meromorphic and periodic on a lattice; equivalently, is meromorphic and has two periods whose ratio is not real. … ►The function is quasi-periodic: for , … ►For further quasi-periodic properties of the -function see Lawden (1989, §6.2).18: 22.2 Definitions
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►As a function of , with fixed , each of the 12 Jacobian elliptic functions is doubly periodic, having two periods whose ratio is not real.
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19: 29.3 Definitions and Basic Properties
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►They are called Lamé functions with real periods and of order
, or more simply, Lamé functions.
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20: 4.2 Definitions
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