Evaluation of double Fermi-Dirac integrals. e.g., ... /y
| F-1/2(x) F-1/2(x) dx
/-∞
or more generally ...
/y
[Γ(m)]-1 | (y-x)m-1 Fj(x) Fk(x) dx = Gm,jk(y) , where m>0.
/-∞
Such integrals arise in calculations of pairwise fermion interactions in condensed matter systems, e.g., when calculating the electron EM exchange energy (see, e.g., the 'specfunc.ElectronDegPres' example and § 80 in Landau and Lifshitz, Statistical Physics Part 1 (3rd edition), 1980).
The values of y and m can be adjusted via the integrand parameters during model runtime. The values of j and k, however, must be chosen before creating (compiling) the integrand (see 'DoubleFDIntegrand').
Note that here -ymax is chosen instead of -∞ since for most such integrals, very little contribution arises from the x<<-1 region.
For values of m<1, care must be taken with the choice of integration routine as a singularity at x=y will appear in the integrand.
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.GNU_ScientificLibrary.Examples.integration.DoubleFDIntegrals.DoubleFDIntegrals