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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 429, Pages 121–139 (Mi znsl6071)  
This article is cited in 12 scientific papers (total in 12 papers)

Representations and inequalities for generalized hypergeometric functions

D. B. Karp

Far Eastern Federal University, Vladivostok, Russia
Full-text PDF (224 kB) Citations (12)
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Abstract: 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.
Key words and phrases: generalized hypergeometric function, Meijer's $G$-function, generalized Stieltjes transform, Laplace transform, complete monotonicity, log-convexity, Luke's inequalities.
Received: 08.09.2014
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 207, Issue 6, Pages 885–897
DOI: https://doi.org/10.1007/s10958-015-2412-7
Bibliographic databases:
Document Type: Article
UDC: 517.58
Language: English
Citation: D. B. Karp, “Representations and inequalities for generalized hypergeometric functions”, Analytical theory of numbers and theory of functions. Part 29, Zap. Nauchn. Sem. POMI, 429, POMI, St. Petersburg, 2014, 121–139; J. Math. Sci. (N. Y.), 207:6 (2015), 885–897
Citation in format AMSBIB
\Bibitem{Kar14}
\by D.~B.~Karp
\paper Representations and inequalities for generalized hypergeometric functions
\inbook Analytical theory of numbers and theory of functions. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 429
\pages 121--139
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6071}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 207
\issue 6
\pages 885--897
\crossref{https://doi.org/10.1007/s10958-015-2412-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84949625201}
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  • https://www.mathnet.ru/eng/znsl/v429/p121
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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