Geodesic
On logarithmic concavity of series in gamma ratios
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2014), pp. 70-77

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We find two-sided bounds and prove non-negativeness Taylor coefficients for the Turán determinants power series with coefficients involving the ratio of gamma-functions. We consider such series as functions of simultaneous shifts of the arguments of the gamma-functions located in the numerator and the denominator. These results are then applied to derive new inequalities for the Gauss hypergeometric function, the incomplete normalized beta-function and the generalized hypergeometric series. This communication continues the research of various authors who investigated logarithmic convexity and concavity of hypergeometric functions in parameters.
Keywords: gamma-function, beta-function, Turán inequalities, logarithmic concavity, generalized hypergeometric functions. 
@article{IVM_2014_6_a6,
     author = {S. I. Kalmykov and D. B. Karp},
     title = {On logarithmic concavity of series in gamma ratios},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {70--77},
     publisher = {mathdoc},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_6_a6/}
}
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S. I. Kalmykov; D. B. Karp. On logarithmic concavity of series in gamma ratios. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2014), pp. 70-77. http://geodesic.mathdoc.fr/item/IVM_2014_6_a6/