Editing SSCpt1/Virial (section)

====Some Detailed Examples====

In an [[SSCpt1/Virial/FormFactors#Structural_Form_Factors|accompanying discussion]], we derive detailed expressions for a selected subset of the above structural form factors and corresponding energy terms in the case of spherically symmetric configurations that obey an {{ Template:Math/MP_PolytropicIndex }} = 5 or an {{ Template:Math/MP_PolytropicIndex }} = 1 polytropic equation of state.  The hope is that this will illustrate, in a clear and helpful manner, how the task of calculating form factors is to be carried out, in practice; and, in particular, to provide one nontrivial example for which analytic expressions are derivable.  This should help with the task of debugging numerical algorithms that are designed to calculate structural form factors for more general cases, which cannot be derived analytically.  The limits of integration will be specified in a general enough fashion that the resulting expressions can be applied, not only to the structures of ''isolated'' polytropes, but to [[SSC/Virial/PolytropesSummary#Further_Evaluation_of_n_.3D_5_Polytropic_Structures|''pressure-truncated'' polytropes]] that are embedded in a hot, tenuous external medium and to the [[SSC/Structure/BiPolytropes/Analytic51#Free_Energy|cores of bipolytropes]].