Class fermi_dirac_integ_direct (o2scl)¶
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template<class fp_t = double, class func_t = funct_ld, class internal_fp_t = long double>
class fermi_dirac_integ_direct¶ Compute several Fermi-Dirac integrals useful for non-relativistic fermions by integrating with a higher precision type.
This class performs direct computation of the Fermi-Dirac integral
\[ F_{a}(\mu) = \int_0^{\infty} \frac{x^a}{1+e^{x-\mu}} \, . \]where \( a \in [-1/2,1/2,3/2,2,3] \) . See also o2scl::fermi_dirac_integ_gsl . The integration is handled by an object of type o2scl::fermi_dirac_integ_tl using an integrator of type o2scl::inte_double_exp_boost .Note that the GSL definition of the Fermi-Dirac integral includes an additional factor of \( 1/\Gamma(a+1) \) which is not included here.
Todo
Future: In fermi_dirac_integ_direct, create a new function allowing arbitrary values of ‘a’ in the equation above.
Public Functions
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inline fermi_dirac_integ_direct()¶
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inline void set_tol(const internal_fp_t &tol)¶
Set tolerance.
Public Members
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fermi_dirac_integ_tl<o2scl::inte_double_exp_boost<func_t, internal_fp_t>, internal_fp_t> it¶
The integrator.
Protected Attributes
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internal_fp_t half¶
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internal_fp_t three_half¶
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internal_fp_t three¶
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internal_fp_t two¶
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inline fermi_dirac_integ_direct()¶