Less simple contiguous function relations for hypergeometric functions
\textit{E. Rainville} [Bull. Am. Math. Soc. 51, 714-722 (1945; Zbl 0063.06380)] called a contiguous function relation simple if the coefficients of the relation are constants otherwise less simple. By a contiguous function is meant a function in which exactly one parameter is shifted by \(\pm 1\) from those of the given function and by a linear recurrence relation, a relation which involves some subsets of the set containing the function along with all its contiguous function relations. Considering hypergeometric functions of several variables for a special set of indices, a linear coefficient contiguous function relation is derived. A set of remarks also given to indicate how various changes can be made to extend the results for repeated index, numerator and denominator, for paired indices, for indices of opposite signs and for Kummer's functions.
scientific article; zbMATH DE number 1326529