Antia (1993) gives minimax rational approximations for
, where is the Fermi–Dirac integral
(25.12.14), for the intervals and
. For each there
are three sets of approximations, with relative maximum errors
, , are called the polygamma functions.
…Most properties of these functions follow straightforwardly by differentiation of properties of the psi function.
►In (5.15.2)–(5.15.7) , and for see §25.6(i).
►For see §24.2(i).
►Figure 21.4.1 provides surfaces of the scaled Riemann theta function
…This Riemann matrix originates from the Riemann surface represented by the algebraic curve ; compare §21.7(i).
►For the scaled Riemann theta functions depicted in Figures 21.4.2–21.4.5