The function RDF[i,j,q] gives the radial distribution function g_{i,j}(r), as 
prescribed by the RFA method [S.B. Yuste, A. Santos and M. López de Haro, J. Chem Phys, 108, 3683 (1998)], for a hard-sphere mixture defined by:
->nco=number of species
->eeta=packing fraction
->con=list with the molar fractions of each species,e.g, {x_1,x_2,x_3}, 
        x_1 being the corresponding to the species with the largest diameter
->ratio=list with the diameter ratios, e.g., {1,ratio_2,ratio_3} where 
ratio_n=sigma_n/sigma_1=sigma_n
->alfa=the \[Alpha] (alpha) parameter of the RFA method (it can be obtained by  means of the function ALFA[nco,eeta,con,ratio])

How to use this notebook:
(1) Introduce the  nco, eeta, con , ratio and  alfa values of your hard-sphere
 mixture in the corresponding cell (see below) , and 
(2) Evaluate the next outest cell. 
After this, you can use the function RDF[i,j,r] to evaluate the RFA radial 
distribution function at distance r for species i and j of your mixture.

This cell should be evaluated for each mixture

Here you have to introduce the values of nco, eeta, con , ratio and  alfa 
corresponding to your hard-sphere mixture

For example, here they are the values of our Example 3  (ternary mixture)

nco=3;  
eeta=49/100;
con={1/102,1/102,100/102};
ratio={1,3/10,1/10};

ALFA[nco,eeta,con,ratio] gives \[Alpha]= 0.018370493983291558

alfa=0.018370493983291558;

For example, here they are the values of our Example 1  (binary mixture)

ALFA[nco,eeta,con,ratio] gives \[Alpha]=0.027838955619564247

numterm is a parameter used in the inversion of the Laplace transform G_ij(s).
  A good value is numterm=100, but if you prefer faster calculations  and are 
not very concerned with the precision of the results, try a smaller number . 
For example, numterm=50 leads also to very good results and  halves the  
computation times.

Now  we evaluate the Laplace transform, G_ij(s), of   r*g_ij(r)  as prescribed
 by the RFA method
You must evaluate this cell again if you changes the mixture and/or the value 
of \[Alpha].

G_ij(s) is  inverted numerically.

EXAMPLES

Example 1. A binary mixture with
  nco=2;   
eeta=49/100;
con={1/2,1/2};
ratio={1,3/10};
alfa=0.027838955619564247;

Here we have used numterm=100

{RDF[1,1,1.05],RDF[1,2,0.66],RDF[2,2,0.35]}

Here we have used numterm=50

{RDF[1,1,1.05],RDF[1,2,0.66],RDF[2,2,0.35]}

Example 2. A binary mixture with
nco=2;   
eeta=49/100;
con={1/16,15/16};
ratio={1,3/10};
alfa=0.018859574773073649;

Here we have used numterm=50

{RDF[1,1,1.05],RDF[1,2,0.66],RDF[2,2,0.35]}

{3.47837,4.07452,2.27661}

Example 3. A ternary mixture with
nco=3;  
eeta=49/100;
con={1/102,1/102,100/102};
ratio={1,3/10,1/10};
alfa=0.018370493983291558;

Here we have used numterm=100

{RDF[1,1,1.05],RDF[1,2,0.66],RDF[1,3,0.6],RDF[2,2,0.35],RDF[3,3,0.11]}

Here we have used numterm=50

{RDF[1,1,1.05],RDF[1,2,0.66],RDF[1,3,0.6],RDF[2,2,0.35],RDF[3,3,0.11]}