# §13.1 Special Notation

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

$m$ integer. nonnegative integers. real variables. complex variable. arbitrary small positive constant. Euler’s constant (§5.2(ii)). Gamma function (§5.2(i)). $\ifrac{{\mathop{\Gamma\/}\nolimits^{\prime}}\!\left(x\right)}{\mathop{\Gamma\/% }\nolimits\!\left(x\right)}$.

The main functions treated in this chapter are the Kummer functions $\mathop{M\/}\nolimits\!\left(a,b,z\right)$ and $\mathop{U\/}\nolimits\!\left(a,b,z\right)$, Olver’s function $\mathop{{\mathbf{M}}\/}\nolimits\!\left(a,b,z\right)$, and the Whittaker functions $\mathop{M_{\kappa,\mu}\/}\nolimits\!\left(z\right)$ and $\mathop{W_{\kappa,\mu}\/}\nolimits\!\left(z\right)$.

Other notations are: $\mathop{{{}_{1}F_{1}}\/}\nolimits\!\left(a;b;z\right)$16.2(i)) and $\Phi(a;b;z)$ (Humbert (1920)) for $\mathop{M\/}\nolimits\!\left(a,b,z\right)$; $\Psi(a;b;z)$ (Erdélyi et al. (1953a, §6.5)) for $\mathop{U\/}\nolimits\!\left(a,b,z\right)$; $V(b-a,b,z)$ (Olver (1997b, p. 256)) for $e^{z}\mathop{U\/}\nolimits\!\left(a,b,-z\right)$; $\mathop{\Gamma\/}\nolimits\!\left(1+2\mu\right)\mathscr{M}_{\kappa,\mu}$ (Buchholz (1969, p. 12)) for $\mathop{M_{\kappa,\mu}\/}\nolimits\!\left(z\right)$.

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