کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4616635 1339355 2013 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Log-convexity and log-concavity for series in gamma ratios and applications
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Log-convexity and log-concavity for series in gamma ratios and applications
چکیده انگلیسی

Polynomial sequence {Pm}m≥0{Pm}m≥0 is qq-logarithmically concave if Pm2−Pm+1Pm−1 is a polynomial with nonnegative coefficients for any m≥1m≥1. We introduce an analogue of this notion for formal power series whose coefficients are nonnegative continuous functions of a parameter. Four types of such power series are considered where the parameter dependence is expressed by a ratio of gamma functions. We prove six theorems stating various forms of qq-logarithmic concavity and convexity of these series. The main motivating examples for these investigations are hypergeometric functions. In the last section of the paper we present new inequalities for the Kummer function, the ratio of the Gauss functions and the generalized hypergeometric function obtained as direct applications of the general theorems.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 406, Issue 2, 15 October 2013, Pages 400–418
نویسندگان
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