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arXiv · 1409.3071

Representations and inequalities for generalized hypergeometric functions

Dmitrii Karp
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Abstract

We find an integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace and cosine Fourier transforms. Using positivity conditions for the weight in this representation we establish various new facts regarding generalized hypergeometric functions, including complete monotonicity, log-convexity in upper parameters, monotonicity of ratios and new proofs of Luke's bounds. Besides, we derive two-sided inequalities for the Bessel type hypergeometric functions by using their series representations.

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Dmitrii Karp. 2014-09-10. Representations and inequalities for generalized hypergeometric functions. https://arxiv.org/abs/1409.3071

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