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1: 34.9 Graphical Method
Thus, any analytic expression in the theory, for example equations (34.3.16), (34.4.1), (34.5.15), and (34.7.3), may be represented by a diagram; conversely, any diagram represents an analytic equation. …For specific examples of the graphical method of representing sums involving the 3 j , 6 j , and 9 j symbols, see Varshalovich et al. (1988, Chapters 11, 12) and Lehman and O’Connell (1973, §3.3).
2: 26.19 Mathematical Applications
Examples can be found in Beckenbach (1981), Billera et al. (1996), and Lovász et al. (1995). …
3: How to Cite
For example: …Your readers can then readily locate the item within the book or online (at http://dlmf.nist.gov/5.4.E1 in this example; see Permalinks & Reference numbers). …
4: Guide to Searching the DLMF
Table 1: Query Examples
Query Matching records contain
Wildcards allow matching patterns and marking parts of an expression that don’t matter (as for example, which variable name the author uses for a function): … For example, the expression Ai 2 + Bi 2 does not occur verbatim in DLMF, but Ai 2 ( z ) + Bi 2 ( z ) and Ai 2 ( x ) + Bi 2 ( x ) do. … For example, for the Bessel function K n ( z ) , you can write K_n(z), BesselK_n(z), BesselK(n,z), or BesselK[n,z]. … For example, you may want equations that contain trigonometric functions, but you don’t care which trigonometric function. …
5: 26.2 Basic Definitions
If, for example, a permutation of the integers 1 through 6 is denoted by 256413 , then the cycles are ( 1 , 2 , 5 ) , ( 3 , 6 ) , and ( 4 ) . … For an example see Figure 26.9.2. … As an example, { 1 , 3 , 4 } , { 2 , 6 } , { 5 } is a partition of { 1 , 2 , 3 , 4 , 5 , 6 } . … As an example, { 1 , 1 , 1 , 2 , 4 , 4 } is a partition of 13. … The example { 1 , 1 , 1 , 2 , 4 , 4 } has six parts, three of which equal 1. …
6: 27.15 Chinese Remainder Theorem
For example, suppose a lengthy calculation involves many 10-digit integers. …Choose four relatively prime moduli m 1 , m 2 , m 3 , and m 4 of five digits each, for example 2 16 - 3 , 2 16 - 1 , 2 16 + 1 , and 2 16 + 3 . …
7: 10.76 Approximations
Because of the comprehensive nature of more recent software packages (§10.77), the following subsections include only references that give representative examples of the kind of approximations that can be used to generate the functions that appear in the present chapter. For references to other approximations, see, for example, Luke (1975, §9.13.3). …
8: 9.16 Physical Applications
Examples dealing with the propagation of light and with radiation of electromagnetic waves are given in Landau and Lifshitz (1962). … These examples of transitions to turbulence are presented in detail in Drazin and Reid (1981) with the problem of hydrodynamic stability. … An example from quantum mechanics is given in Landau and Lifshitz (1965), in which the exact solution of the Schrödinger equation for the motion of a particle in a homogeneous external field is expressed in terms of Ai ( x ) . …This reference provides several examples of applications to problems in quantum mechanics in which Airy functions give uniform asymptotic approximations, valid in the neighborhood of a turning point. …
9: 12.16 Mathematical Applications
For examples see §§13.20(iii), 13.20(iv), 14.15(v), and 14.26. …
10: 25.17 Physical Applications
Quantum field theory often encounters formally divergent sums that need to be evaluated by a process of regularization: for example, the energy of the electromagnetic vacuum in a confined space (Casimir–Polder effect). …