Geodesic
Representations and inequalities for generalized hypergeometric functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 121-139 Cet article a éte moissonné depuis la source Math-Net.Ru

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An integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace, and cosine Fourier transforms is found. Using positivity conditions for the weight in this representation, 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 are established. In addition, two-sided inequalities for the Bessel type hypergeometric functions are derived with use of their series representations. 
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D. B. Karp. Representations and inequalities for generalized hypergeometric functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 121-139. http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a9/

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