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11: 26.18 Counting Techniques
Example 1
Example 2
Example 3
For further examples in the use of generating functions, see Stanley (1997, 1999) and Wilf (1994). …
12: 26.20 Physical Applications
Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993). …
13: 34.10 Zeros
For further information, including examples of nontrivial zeros and extensions to 9 j symbols, see Srinivasa Rao and Rajeswari (1993, pp. 133–215, 294–295, 299–310).
14: Peter L. Walker
Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004. …
15: 28.17 Stability as x ±
For example, positive real values of a with q = 0 comprise stable pairs, as do values of a and q that correspond to real, but noninteger, values of ν . … For example, as x + one of the solutions me ν ( x , q ) and me ν ( - x , q ) tends to 0 and the other is unbounded (compare Figure 28.13.5). …
16: 23.23 Tables
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 g 2 and g 3 . …
17: 2.2 Transcendental Equations
Example
For exampleFor other examples see de Bruijn (1961, Chapter 2).
18: Mathematical Introduction
See, for example, Chapters 16, 17, 18, 19, 21, 27, 29, 31, 32, 34, 35, and 36. … See, for example, Figures 10.3.110.3.4. … See Figures 10.3.510.3.8 for examples. … See, for example, Figures 5.3.45.3.6. …See, for example, Figures 10.3.910.3.16. …
19: 5.19 Mathematical Applications
Example
The left-hand side of (5.13.1) is a typical example. …For further information and examples see §2.5 and Paris and Kaminski (2001, Chapters 5, 6, and 8). …
20: 3.12 Mathematical Constants
can be defined analytically in numerous ways, for example, …