lattice
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11: 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
…12: 23.19 Interrelations
13: 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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14: 23.13 Zeros
15: 23.11 Integral Representations
16: 23.12 Asymptotic Approximations
17: 31.2 Differential Equations
18: 23.8 Trigonometric Series and Products
19: 26.2 Basic Definitions
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Lattice Path
►A lattice path is a directed path on the plane integer lattice . …For an example see Figure 26.9.2. ►A k-dimensional lattice path is a directed path composed of segments that connect vertices in so that each segment increases one coordinate by exactly one unit. …20: 16.24 Physical Applications
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