CONVEXITY AND INEQUALITIES RELATED TO EXTENDED BETA AND CONFLUENT HYPERGEOMETRIC FUNCTIONS

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

1 Tianjin Polytechnic University
2 Henan Polytechnic University
3 Inner Mongolia University for Nationalities
4 2IU - International Islamic University [Islamabad, Pakistan]
5 PSAU - Prince Sattam Bin Abdul-Aziz 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; extended confluent hypergeometric function; inequality; extended beta function; logarithmic convexity

Domaines: Analyse classique [math.CA]

Feng Qi, Gauhar Rahman, Kottakkaran Sooppy Nisar. CONVEXITY AND INEQUALITIES RELATED TO EXTENDED BETA AND CONFLUENT HYPERGEOMETRIC FUNCTIONS: Inequalities for confluent hypergeometric functions. 2018. ⟨hal-01703900v1⟩