The Newton Polyhedron and Positivity of F-2(3) Hypergeometric Functions

초록

As for the F-2(3) hypergeometric function of the form F-2(3) [(a1, a2)(b1, b2, b3)vertical bar - x(2)] (x > 0), where all of parameters are assumed to be positive, we give sufficient conditions on (b(1), b(2), b(3)) for its positivity in terms of Newton polyhedra with vertices consisting of permutations of (a(2), a(1) + 1/2, 2a(1)) or (a(1), a(2) + 1/2, 2a(2)). As an application, we obtain an extensive validity region of (alpha, lambda, mu) for the inequality integral(x)(0) (x - t)(lambda) t(mu) J(alpha)(t) dt >= 0 (x > 0).

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