As for the positivity of 1 F 2 generalized hypergeometric functions, we present a list of necessary and sufficient conditions in terms of parameters and determine the region of positivity by certain Newton diagram.

We present a rational extension of Newton diagram for the positivity of 1 F 2 generalized hypergeometric functions. As an application, we give upper and lower bounds for the transcendental roots β(α) ofwhere j α,2 denotes the second positive zero of Bessel function J α .

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As to the Bessel integrals of typewe improve known positivity results by making use of new positivity criteria for 1 F 2 and 2 F 3 generalized hypergeometric functions. As an application, we extend Buhmann's class of compactly supported radial basis functions.