Geodesic
Inequalities for some basic hypergeometric functions
Problemy analiza, Tome 8 (2019) no. 1, pp. 47-64

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We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric functions with respect to the simultaneous shift of all its parameters. For a particular case of Heine's basic hypergeometric function, we prove logarithmic concavity and convexity with respect to the bottom parameter. We, further, establish a linearization identity for the generalized Turánian formed by a particular case of Heine's basic hypergeometric function. Its $q=1$ case also appears to be new.
Keywords: basic hypergeometric function, log-convexity, log-concavity, multiplicative concavity, generalized Turánian, $q$-hypergeometric identity. 
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     author = {S. I. Kalmykov and D. B. Karp},
     title = {Inequalities for some basic hypergeometric functions},
     journal = {Problemy analiza},
     pages = {47--64},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_1_a3/}
}
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S. I. Kalmykov; D. B. Karp. Inequalities for some basic hypergeometric functions. Problemy analiza, Tome 8 (2019) no. 1, pp. 47-64. http://geodesic.mathdoc.fr/item/PA_2019_8_1_a3/