1 Type Signatures

Table 1: Types used in the special function type signature, where

\mathscr{T}

stands for any arbitrary set or type.

Notation	Meaning
$\mathscr{T}\to\mathscr{T}^{\prime}$	function (mapping) from type $\mathscr{T}$ to $\mathscr{T}^{\prime}$
$\mathscr{T}\times\mathscr{T}^{\prime}$	product set of multiple types
$\mathbb{R}$	the set of real numbers (excluding $\infty$ )
$\mathbb{C}$	the set of complex numbers (excluding $\infty$ )
$\mathbb{Z}$	the set of integers
${\mathbb{Z}^{+}}$	the set of integers $>0$
${\mathbb{Z}^{*}}$	the set of integers $\geq 0$
$\mathbb{Q}$	rational numbers
$\mathbb{D}$	the complex numbers in the open unit disc, $\|z\|<1$
$\left\{a_{0},\ldots\right\}$	one of a finite set (of symbols)
${\mathscr{T}}^{n}$	$n$ -tuples with elements of type $\mathscr{T}$
	(eg. ${\mathbb{R}}^{2}$ for pairs of reals)
${\mathscr{T}}^{\bullet}$	tuples with elements of type $\mathscr{T}$ , unspecified length
${\mathscr{T}}^{n}$	vectors of dimension $n$ , with elements of type $\mathscr{T}$
${\mathscr{T}}^{\bullet}$	vectors with elements of type $\mathscr{T}$ , unspecified dimension
${\mathscr{T}}^{n\times m}$	$n\times m$ matrices with elements of type $\mathscr{T}$
${\mathscr{T}}^{\bullet\times\bullet}$	matrices with elements of type $\mathscr{T}$ (unspecified dimension)
$\mathbf{L}$	lattices in the complex plane (in the sense of elliptic functions