cycle notation

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21: 28.1 Special Notation

§28.1 Special Notation

►(For other notation see Notation for the Special Functions.) … ►The notation for the joining factors is … ►Alternative notations for the parameters

a

and

q

are shown in Table 28.1.1. … ►Alternative notations for the functions are as follows. …

22: 10.1 Special Notation

§10.1 Special Notation

►(For other notation see Notation for the Special Functions.) … ►A common alternative notation for

Y_{\nu}\left(z\right)

N_{\nu}(z)

. Other notations that have been used are as follows. … ►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).

23: 36.1 Special Notation

§36.1 Special Notation

►(For other notation see Notation for the Special Functions.) …

24: 13.1 Special Notation

§13.1 Special Notation

►(For other notation see Notation for the Special Functions.) … ► ►Other notations are:

{{}_{1}F_{1}}\left(a;b;z\right)

(§16.2(i)) and

\Phi(a;b;z)

(Humbert (1920)) for

M\left(a,b,z\right)

;

\Psi(a;b;z)

(Erdélyi et al. (1953a, §6.5)) for

U\left(a,b,z\right)

;

V(b-a,b,z)

(Olver (1997b, p. 256)) for

e^{z}U\left(a,b,-z\right)

;

\Gamma\left(1+2\mu\right)\mathscr{M}_{\kappa,\mu}

(Buchholz (1969, p. 12)) for

M_{\kappa,\mu}\left(z\right)

. … ►For an historical account of notations see Slater (1960, Chapter 1). …

25: 3.6 Linear Difference Equations

… ►If agreement is not within a prescribed tolerance the cycle is continued. … ►In the notation of §3.6(v) we have

M=10

and

\epsilon=\tfrac{1}{2}\times 10^{-8}

. …

►(For other notation see Notation for the Special Functions.) … ► … ►These notations agree with Gasper and Rahman (2004). A slightly different notation is that in Bailey (1964) and Slater (1966); see §17.4(i). …

27: 27.1 Special Notation

§27.1 Special Notation

►(For other notation see Notation for the Special Functions.) …

28: 27 Functions of Number Theory

…

29: 33.1 Special Notation

§33.1 Special Notation

►(For other notation see Notation for the Special Functions.) … ►

Alternative Notations

►

Curtis (1964a):

$P_{\ell}(\epsilon,r)=(2\ell+1)!f\left(\epsilon,\ell;r\right)/2^{\ell+1}$ , $Q_{\ell}(\epsilon,r)=-(2\ell+1)!h\left(\epsilon,\ell;r\right)/(2^{\ell+1}A(% \epsilon,\ell))$ .

►

Greene et al. (1979):

$f^{(0)}(\epsilon,\ell;r)=f\left(\epsilon,\ell;r\right)$ , $f(\epsilon,\ell;r)=s\left(\epsilon,\ell;r\right)$ , $g(\epsilon,\ell;r)=c\left(\epsilon,\ell;r\right)$ .

30: 34.1 Special Notation

§34.1 Special Notation

►(For other notation see Notation for the Special Functions.) ► ►►

$2j_{1},2j_{2},2j_{3},2l_{1},2l_{2},2l_{3}$	nonnegative integers.
…

… ►

34.1.1

\left(j_{1}\;m_{1}\;j_{2}\;m_{2}|j_{1}\;j_{2}\;j_{3}\,\,m_{3}\right)=(-1)^{j_{% 1}-j_{2}+m_{3}}(2j_{3}+1)^{\frac{1}{2}}\begin{pmatrix}j_{1}&j_{2}&j_{3}\\ m_{1}&m_{2}&-m_{3}\end{pmatrix};

ⓘ

Symbols:: $\begin{pmatrix}\NVar{j_{1}}&\NVar{j_{2}}&\NVar{j_{3}}\\ \NVar{m_{1}}&\NVar{m_{2}}&\NVar{m_{3}}\end{pmatrix}$ : $\mathit{3j}$ symbol and $j,j_{r}$ : non-negative integers or non-negative integers plus one half.
Sources:: Edmonds (1974, p. 46, Eq. (3.7.3)); Rotenberg et al. (1959, p. 1, Eq. (1.1a))
Permalink:: http://dlmf.nist.gov/34.1.E1
Encodings:: pMML, png, TeX
Clarification (effective with 1.0.15):: A wording change reflects that the Clebsch–Gordan coefficients are an alternative formulation of angular momentum problems, rather than alternative notation for the $\mathit{3j}$ . The sign of $m_{3}$ was changed for clarity.
See also:: Annotations for §34.1 and Ch.34

… ►For other notations for

\mathit{3j}

\mathit{6j}

\mathit{9j}

symbols, see Edmonds (1974, pp. 52, 97, 104–105) and Varshalovich et al. (1988, §§8.11, 9.10, 10.10).