  In this article we developed a special topic of our pure-mathematics papers
concerning the hypergeometric theory. Based upon a Roberts's reduction approach
of hyperelliptic integrals to elliptic ones and on the simultaneous
multivariable hypergeometric series evaluation of them, several identities have
been obtained expressing $\pi$ in terms of special values of elliptic,
hypergeometric and Gamma functions. By them $\pi$ can be provided through
either only one or two parameters and through the imaginary unit. In any case,
such results, all unpublished and undoubtably new, will provide, beyond their
own beauty, a useful tool in order to check the routines (more or less naive)
which one can build for the practical computations of Lauricella's functions
met frequently in researches on Mechanics or Elasticity.
