# Revision history [back]

### Analytical evaluation of Fermi-Dirac integrals

It seems that sagemath is unable to calculate Fermic-Dirac type integrals, e. g. integrate(x^2/(1+ e^x),x,0,oo) => limit(1/3x^3 - x^2log(e^x + 1) - 2xdilog(-e^x) + 2polylog(3, -e^x), x, +Infinity, minus) + 3/2zeta(3)

integrate(x^3/(1+ e^x),x,0,oo)==> -7/120pi^4 + limit(1/4x^4 - x^3log(e^x + 1) - 3x^2dilog(-e^x) + 6xpolylog(3, -e^x) - 6polylog(4, -e^x), x, +Infinity, minus)

Normally, the frormer valuates to (3Zeta)/2 and the latter to (7Pi^4)/120, using Mathematica. 2 None FrédéricC 5114 ●3 ●42 ●111

### Analytical evaluation of Fermi-Dirac integrals

It seems that sagemath is unable to calculate Fermic-Dirac type integrals, e. g.

integrate(x^2/(1+ e^x),x,0,oo) =>
limit(1/3x^3 limit(1/3*x^3 - x^2log(e^x x^2*log(e^x + 1) - 2xdilog(-e^x) 2*x*dilog(-e^x) + 2polylog(3, 2*polylog(3, -e^x), x, +Infinity, minus) + 3/2zeta(3)3/2*zeta(3)
integrate(x^3/(1+ e^x),x,0,oo)==>
-7/120pi^4 -7/120*pi^4 + limit(1/4x^4 limit(1/4*x^4 - x^3log(e^x x^3*log(e^x + 1) - 3x^2dilog(-e^x) 3*x^2*dilog(-e^x) + 6xpolylog(3, 6*x*polylog(3, -e^x) - 6polylog(4, 6*polylog(4, -e^x), x,  +Infinity, minus)minus)


Normally, the frormer valuates to (3Zeta)/2 and the latter to (7Pi^4)/120, using Mathematica.

### Analytical evaluation of Fermi-Dirac integrals

It seems that sagemath is unable to calculate Fermic-Dirac type integrals, e. g.

integrate(x^2/(1+ e^x),x,0,oo) =>
limit(1/3*x^3 - x^2*log(e^x + 1) - 2*x*dilog(-e^x) + 2*polylog(3, -e^x), x, +Infinity, minus) + 3/2*zeta(3)

integrate(x^3/(1+ e^x),x,0,oo)==>
-7/120*pi^4 + limit(1/4*x^4 - x^3*log(e^x + 1) - 3*x^2*dilog(-e^x) + 6*x*polylog(3, -e^x) - 6*polylog(4, -e^x), x,
+Infinity, minus)


Normally, the frormer valuates former evaluates to (3Zeta)/2 and the latter to (7Pi^4)/120, using Mathematica.