Contiguous relations of hypergeometric series (Q1874187)

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 dependent (over the field of rational functions in the parameters). The author proves several coefficient properties of these general contiguous relations, and uses the results to propose effective ways to compute contiguous relations. He also discusses contiguous relations of generalized and basic hypergeometric functions, and several applications of them.