Abstract
It is a classical problem to find contiguous relations of hypergeometric functions of several variables. Recently Kametaka [11] and Okamoto [15] have developed the theory of hypergeometric solutions of the Toda equation. We need to find the explicit formulas of contiguous relations (or ladders) to construct the hypergeometric solutions of the Toda equation explicitly. We present an algorithm to obtain contiguous relations of hypergeometric functions of several variables. The algorithm is based on Buchberger’s algorithm [3] on the Gröbner basis.
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Takayama, N. Gröbner basis and the problem of contiguous relations. Japan J. Appl. Math. 6, 147–160 (1989). https://doi.org/10.1007/BF03167920
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DOI: https://doi.org/10.1007/BF03167920