# §15.1 Special Notation

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

$x$ real variable. complex variable. real or complex parameters. integers. nonnegative integer. arbitrary small positive constant. gamma function (§5.2(i)). $\ifrac{{\mathop{\Gamma\/}\nolimits^{\prime}}\!\left(z\right)}{\mathop{\Gamma\/% }\nolimits\!\left(z\right)}$.

Unless indicated otherwise primes denote derivatives with respect to the variable.

We use the following notations for the hypergeometric function:

 15.1.1 $\mathop{{{}_{2}F_{1}}\/}\nolimits\!\left(a,b;c;z\right)=\mathop{F\/}\nolimits% \!\left(a,b;c;z\right)=\mathop{F\/}\nolimits\!\left({a,b\atop c};z\right),$

and also

 15.1.2 $\frac{\mathop{F\/}\nolimits\!\left(a,b;c;z\right)}{\mathop{\Gamma\/}\nolimits% \!\left(c\right)}=\mathop{\mathbf{F}\/}\nolimits\!\left(a,b;c;z\right)=\mathop% {\mathbf{F}\/}\nolimits\!\left({a,b\atop c};z\right)=\mathop{{{}_{2}{\mathbf{F% }}_{1}}\/}\nolimits\!\left(a,b;c;z\right),$

(Olver (1997b, Chapter 5)).