On some new contiguous relations for the Gauss hypergeometric function with applications

Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a new set of contiguous function relations are established. Applications of such relations to hypergeometric summation formulas and the theory of Jacobi polynomials are presented.