Antia (1993) gives minimax rational approximations for
, where is the Fermi–Dirac integral
(25.12.14), for the intervals and
, with
. For each there
are three sets of approximations, with relative maximum errors
.
►The functions
, , 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
, with
…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
…
►►
►Figure 21.4.5: The real part of a genus 3 scaled Riemann theta function: , , .
…
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