Dmitrii Karp
Published 2014-09-10Version 1
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.
Comments: 13 pages, no figures
Inequalities and monotonicity of ratios for generalized hypergeometric function
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Symmetric polynomials and $l^p$ inequalities for certain intervals of $p$
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