Class polylog (o2scl)¶
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class
o2scl
::
polylog
¶ Class to compute the polylogarithm function.
This class uses long double arithmetic and integral representations to compute the polylog functions.
- Note
experimental
The relationship between the polylogarithm and the Fermi-Dirac distribution is:
\[ \mathrm{Li}_{1+s}(-e^{\mu}) = - \frac{1}{\Gamma(s+1)} \int_0^{\infty} \frac{k^{s}}{e^{k-\mu}+1} \]or\[ \mathrm{Li}_{s}(z) = - \frac{1}{\Gamma(s)} \int_0^{\infty} \frac{k^{s-1}}{e^{k-\ln(-z)}+1} \]this representation works for negative values of \( z \).The relationship between the polylogarithm and the Bose-Einstein distribution is:
\[ \mathrm{Li}_{1+s}(e^{\mu}) = \frac{1}{\Gamma(s+1)} \int_0^{\infty} \frac{k^{s}}{e^{k-\mu}-1} \]or\[ \mathrm{Li}_{s}(z) = \frac{1}{\Gamma(s)} \int_0^{\infty} \frac{k^{s-1}}{e^{k-\ln(z)}-1} \]this representation works for positive values of \( z \).Public Functions
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polylog
()¶
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void
set_tol
(double tol)¶
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double
calc
(double s, double y)¶ Polylogarithm function.
Protected Attributes
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fermi_dirac_integ_tl<o2scl::inte_exp_sinh_boost<funct_ld, 15, long double>, long double>
it
¶ The integrator for negative arguments.
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bose_einstein_integ_tl<o2scl::inte_exp_sinh_boost<funct_ld, 15, long double>, long double>
it2
¶ The integrator for positive arguments.