Weierstrass%20product
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1: 23.2 Definitions and Periodic Properties
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§23.2(i) Lattices
… ► … ►§23.2(ii) Weierstrass Elliptic Functions
… ► ►§23.2(iii) Periodicity
…2: 23.14 Integrals
3: 23.10 Addition Theorems and Other Identities
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§23.10(i) Addition Theorems
… ►§23.10(ii) Duplication Formulas
… ►(23.10.8) continues to hold when , , are permuted cyclically. … ►§23.10(iii) -Tuple Formulas
… ►§23.10(iv) Homogeneity
…4: 23.1 Special Notation
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►The main functions treated in this chapter are the Weierstrass
-function ; the Weierstrass zeta function ; the Weierstrass sigma function ; the elliptic modular function ; Klein’s complete invariant ; Dedekind’s eta function .
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lattice in . | |
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nome. | |
discriminant . | |
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Cartesian product of groups and , that is, the set of all pairs of elements with group operation . |
5: 23.9 Laurent and Other Power Series
§23.9 Laurent and Other Power Series
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23.9.6
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►Also, Abramowitz and Stegun (1964, (18.5.25)) supplies the first 22 terms in the reverted form of (23.9.2) as .
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6: 23 Weierstrass Elliptic and Modular
Functions
Chapter 23 Weierstrass Elliptic and Modular Functions
…7: 23.8 Trigonometric Series and Products
§23.8 Trigonometric Series and Products
►§23.8(i) Fourier Series
… ►§23.8(ii) Series of Cosecants and Cotangents
… ►where in (23.8.4) the terms in and are to be bracketed together (the Eisenstein convention or principal value: see Weil (1999, p. 6) or Walker (1996, p. 3)). … ►§23.8(iii) Infinite Products
…8: 23.3 Differential Equations
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►The lattice invariants are defined by
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►and are denoted by .
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►Similarly for and .
As functions of and , and are meromorphic and is entire.
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