A numerical method to extract ΛQCD using hypergeometrical functions

The solutions for DGLAP evolution equations are considered numerically based on Laguerre polynomials expansion. We prepare some FORTRAN codes and subroutines based on Monte Carlo method which yields us reasonable results for parton densities at high energy scales. The techniques to write the codes can be used for other numerical computations. Our results for parton densities are in good agreement with GRSV and CTEQ phenomenological groups. They are also better with respect to what have been represented by other people, especially for sea and gluon densities. All the stages of computations have been done completely in a numerical way. Our results have sufficient stability after doing few iterations. This indicates that Laguerre polynomials contain reliable algebraic strucute to use them for the numerical solutions. In continuation by comparison the evolved nucleon structure, based on Jaccobi polynomials expansion with the similar function which are arising from the evolved parton densities using the Laguerre polynomials expansion, we are able to extract the numerical value of QCD cut off parameter.