functions in fermi.i -

             fd12(x)  
 
    return Fermi-Dirac integral of order 1/2,  
       fd12(x) = integral[0 to inf]{ dt * t^0.5 / (exp(t-x)+1) }  
    accurate to about 1e-12  

             fd32(x)  
 
    return Fermi-Dirac integral of order 3/2,  
       fd32(x) = integral[0 to inf]{ dt * t^1.5 / (exp(t-x)+1) }  
    accurate to about 1e-12  

             fd52(x)  
 
    return Fermi-Dirac integral of order 5/2,  
       fd52(x) = integral[0 to inf]{ dt * t^2.5 / (exp(t-x)+1) }  
    accurate to about 1e-12  

             fdm12(x)  
 
    return Fermi-Dirac integral of order -1/2,  
       fdm12(x) = integral[0 to inf]{ dt * t^-0.5 / (exp(t-x)+1) }  
    accurate to about 1e-12  

             #include "fermi.i"  
 
    Fermi-Dirac integrals and inverses of orders -1/2, 1/2, 3/2, 5/2  
    
    Antia, H. M., Aph.J. 84, p.101-108 (1993)  
    

             ifd12(y)  
 
    return x = inverse of Fermi-Dirac integral of order 1/2,  
       y = integral[0 to inf]{ dt * t^0.5 / (exp(t-x)+1) }  
    accurate to about 1e-8  

             ifd32(y)  
 
    return x = inverse of Fermi-Dirac integral of order 3/2,  
       y = integral[0 to inf]{ dt * t^1.5 / (exp(t-x)+1) }  
    accurate to about 1e-8  

             ifd52(y)  
 
    return x = inverse of Fermi-Dirac integral of order 5/2,  
       y = integral[0 to inf]{ dt * t^2.5 / (exp(t-x)+1) }  
    accurate to about 1e-8  

             ifdm12(y)  
 
    return x = inverse of Fermi-Dirac integral of order -1/2,  
       y = integral[0 to inf]{ dt * t^-0.5 / (exp(t-x)+1) }  
    accurate to about 1e-8