  The 15 Gauss contiguous relations for ${}_2F_1$ hypergeometric series imply
that any three ${}_2F_1$ series whose corresponding parameters differ by
integers are linearly related (over the field of rational functions in the
parameters). We prove several properties of coefficients of these general
contiguous relations, and use the results to propose effective ways to compute
contiguous relations. We also discuss contiguous relations of generalized and
basic hypergeometric functions, and several applications of them.
