Convexity and inequalities related to extended beta and confluent hypergeometric functions

Feng Qi; Kottakkaran Sooppy Nisar; Gauhar Rahman; Feng Qi; Kottakkaran Sooppy Nisar; Gauhar Rahman

doi:10.3934/math.2019.5.1499

AIMS Mathematics

2019, Volume 4, Issue 5: 1499-1507. doi: 10.3934/math.2019.5.1499

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Research article

Convexity and inequalities related to extended beta and confluent hypergeometric functions

1.
College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China
2.
School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
3.
Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, China
4.
Department of Mathematics, College of Arts and Science at Wadi Al Dawaser, Prince Sattam bin Abdulaziz University, Wadi Al Dawaser 11991, Kingdom of Saudi Arabia
5.
Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal 18000, Upper Dir, Pakistan

Received: 17 July 2019 Accepted: 05 September 2019 Published: 23 September 2019
MSC : Primary 33B15; Secondary 26D15, 33B99

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.
- extended beta function,
- extended confluent hypergeometric function,
- inequality,
- logarithmic convexity,
- monotonicity
Citation: Feng Qi, Kottakkaran Sooppy Nisar, Gauhar Rahman. Convexity and inequalities related to extended beta and confluent hypergeometric functions[J]. AIMS Mathematics, 2019, 4(5): 1499-1507. doi: 10.3934/math.2019.5.1499

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Abstract

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.

References

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