Convexity and inequalities related to extended beta and confluent hypergeometric functions

Feng Qi (1, 2, 3) , Kottakkaran Sooppy Nisar (4) , Gauhar Rahman (5)

1 Tianjin Polytechnic University
2 Henan Polytechnic University
3 Inner Mongolia University for Nationalities
4 PSAU - Prince Sattam Bin Abdul-Aziz University
5 Shaheed Benazir Bhutto University

In the paper, the authors establish the logarithmic convexity and some inequalities for the extended beta function and, by using these inequalities for the extended beta function, find the logarithmic convexity and the monotonicity for the extended confluent hypergeometric function.

Mots clés: monotonicity; logarithmic convexity; extended confluent hypergeometric function; extended beta function; inequality

Domaines: Analyse classique [math.CA]

Feng Qi, Kottakkaran Sooppy Nisar, Gauhar Rahman. Convexity and inequalities related to extended beta and confluent hypergeometric functions. AIMS Mathematics, 2019, 4 (5), pp.1499--1507. ⟨10.3934/math.2019.5.1499⟩. ⟨hal-01703900v2⟩