§31.1 Special Notation

Keywords:: Heun functions, Heun’s equation
Permalink:: http://dlmf.nist.gov/31.1

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

$x$ , $y$	real variables.
$z$ , $\zeta$ , $w$ , $W$	complex variables.
$j$ , $k$ , $\ell$ , $m$ , $n$	nonnegative integers.
$a$	complex parameter, $\|a\|\geq 1,a\neq 1$ .
$q,\alpha,\beta,\gamma,\delta,\epsilon,\nu$	complex parameters.

The main functions treated in this chapter are $\mathop{\mathit{H\!\ell}\/}\nolimits\!\left(a,q;\alpha,\beta,\gamma,\delta;z\right)$ , $\mathop{(s_{1},s_{2})\mathit{Hf}_{{m}}\/}\nolimits\!\left(a,q_{m};\alpha,\beta,\gamma,\delta;z\right)$ , $\mathop{(s_{1},s_{2})\mathit{Hf}_{{m}}^{{\nu}}\/}\nolimits\!\left(a,q_{m};\alpha,\beta,\gamma,\delta;z\right)$ , and the polynomial $\mathop{\mathit{Hp}_{{n,m}}\/}\nolimits\!\left(a,q_{{n,m}};-n,\beta,\gamma,\delta;z\right)$ . These notations were introduced by Arscott in Ronveaux (1995, pp. 34–44). Sometimes the parameters are suppressed.