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11: 11.1 Special Notation

§11.1 Special Notation

►(For other notation see Notation for the Special Functions.) … ►For the functions $J_{\nu }\left(z\right)$, $Y_{\nu }\left(z\right)$, $H_{\nu }^{(1)}\left(z\right)$, $H_{\nu }^{(2)}\left(z\right)$, $I_{\nu }\left(z\right)$, and $K_{\nu }\left(z\right)$ see §§10.2(ii), 10.25(ii). …

12: 26.1 Special Notation

§26.1 Special Notation

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

Alternative Notations

… ►Other notations for $s(n,k)$, the Stirling numbers of the first kind, include $S_n^{(k)}$ (Abramowitz and Stegun (1964, Chapter 24), Fort (1948)), $S_n^k$ (Jordan (1939), Moser and Wyman (1958a)), $\left(\genfrac{}{}{0.0pt}{}{n-1}{k-1}\right)B_{n-k}^{(n)}$ (Milne-Thomson (1933)), ${(-1)}^{n-k}{S}_1(n-1,n-k)$ (Carlitz (1960), Gould (1960)), ${(-1)}^{n-k}\left[\genfrac{}{}{0pt}{}{n}{k}\right]$ (Knuth (1992), Graham et al. (1994), Rosen et al. (2000)). ►Other notations for $S(n,k)$, the Stirling numbers of the second kind, include ${𝒮}_n^{(k)}$ (Fort (1948)), ${𝔖}_n^k$ (Jordan (1939)), ${\sigma }_n^k$ (Moser and Wyman (1958b)), $\left(\genfrac{}{}{0.0pt}{}{n}{k}\right)B_{n-k}^{(-k)}$ (Milne-Thomson (1933)), $S_2(k,n-k)$ (Carlitz (1960), Gould (1960)), $\left\{\genfrac{}{}{0pt}{}{n}{k}\right\}$ (Knuth (1992), Graham et al. (1994), Rosen et al. (2000)), and also an unconventional symbol in Abramowitz and Stegun (1964, Chapter 24).

13: 22.1 Special Notation

§22.1 Special Notation

►(For other notation see Notation for the Special Functions.) … ► ►The notation $\mathrm{sn}(z,k)$, $\mathrm{cn}(z,k)$, $\mathrm{dn}(z,k)$ is due to Gudermann (1838), following Jacobi (1827); that for the subsidiary functions is due to Glaisher (1882). Other notations for $\mathrm{sn}(z,k)$ are $\mathrm{sn}(z|m)$ and $\mathrm{sn}(z,m)$ with $m=k^2$; see Abramowitz and Stegun (1964) and Walker (1996). …

14: 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. …

15: 10.1 Special Notation

§10.1 Special Notation

►(For other notation see Notation for the Special Functions.) … ►A common alternative notation for $Y_{\nu }\left(z\right)$ is $N_{\nu }(z)$. 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).

16: 36.1 Special Notation

§36.1 Special Notation

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

17: 13.1 Special Notation

§13.1 Special Notation

►(For other notation see Notation for the Special Functions.) … ► ►Other notations are: ${}_1{}^{}F_1^{}(a;b;z)$ (§16.2(i)) and $\mathrm{\Phi }(a;b;z)$ (Humbert (1920)) for $M(a,b,z)$; $\mathrm{\Psi }(a;b;z)$ (Erdélyi et al. (1953a, §6.5)) for $U(a,b,z)$; $V(b-a,b,z)$ (Olver (1997b, p. 256)) for ${\mathrm{e}}^{z}U(a,b,-z)$; $\mathrm{\Gamma }\left(1+2\mu \right){ℳ}_{\kappa ,\mu }$ (Buchholz (1969, p. 12)) for $M_{\kappa ,\mu }\left(z\right)$. … ►For an historical account of notations see Slater (1960, Chapter 1). …

18: 17.1 Special Notation

§17.1 Special Notation

►(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). …

19: 27.1 Special Notation

§27.1 Special Notation

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

20: 27 Functions of Number Theory

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