caa a22 4500 605522510 CHVBK 20210128100745.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10958-015-2412-7 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2412-7 Karp D. Far Eastern Federal University, Vladivostok, Russia aut Representations and Inequalities for Generalized Hypergeometric Functions [Elektronische Daten] [D. Karp] 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 the use of their series representations. Bibliography: 22 titles. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 207/6(2015-06-01), 885-897 1072-3374 207:6<885 2015 207 10958 https://doi.org/10.1007/s10958-015-2412-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2412-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Karp D. Far Eastern Federal University, Vladivostok, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 207/6(2015-06-01), 885-897 1072-3374 207:6<885 2015 207 10958