lattice walks
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11: 23.23 Tables
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►2 in Abramowitz and Stegun (1964) gives values of , , and to 7 or 8D in the rectangular and rhombic cases, normalized so that and (rectangular case), or and (rhombic case), for = 1.
…05, and in the case of the user may deduce values for complex by application of the addition theorem (23.10.1).
►Abramowitz and Stegun (1964) also includes other tables to assist the computation of the Weierstrass functions, for example, the generators as functions of the lattice invariants and .
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12: 23.6 Relations to Other Functions
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►In this subsection , are any pair of generators of the lattice
, and the lattice roots , , are given by (23.3.9).
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►For further results for the -function see Lawden (1989, §6.2).
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►Again, in Equations (23.6.16)–(23.6.26), are any pair of generators of the lattice
and are given by (23.3.9).
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Rectangular Lattice
… ►General Lattice
…13: 23.19 Interrelations
14: 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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►Abramowitz and Stegun (1964, Chapter 18) considers only rectangular and rhombic lattices (§23.5); , are replaced by , for the former and by , for the latter.
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lattice in . | |
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lattice generators (). | |
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discriminant . | |
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