SOME INEQUALITIES INVOLVING THE EXTENDED GAMMA AND BETA FUNCTIONS
Nisar, Kottakkaran Sooppy ; Qi, Feng ; Rahman, Gauhar ; Mubeen, Shahid ; Arshad, Muhammad
HAL, hal-01701647 / Harvested from HAL
Text on HAL
In the paper, the authors present some inequalities involving the extended gamma and beta functions via some classical inequalities such as Chebychev's inequality for synchronous (or asynchronous respectively) mappings, give a new proof of the log-convexity of the extended gamma and beta functions by using the H\"older inequality, and introduce a Tur\'an type mean inequality for the Kummer confluent $k$-hypergeometric function.
Publié le : 2018-02-06
Classification:  inequality,  extended beta function,  extended gamma function,  confluent hypergeometric $k$-function,  logarithmic convexity,  MSC: Primary 33B15; Secondary 33C15, 33B20, 33C05, 41A60,  [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] 
@article{hal-01701647,
     author = {Nisar, Kottakkaran Sooppy  and Qi, Feng and Rahman, Gauhar  and Mubeen, Shahid  and Arshad, Muhammad},
     title = {SOME INEQUALITIES INVOLVING THE EXTENDED GAMMA AND BETA FUNCTIONS},
     journal = {HAL},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01701647}
}

Nisar, Kottakkaran Sooppy ; Qi, Feng; Rahman, Gauhar ; Mubeen, Shahid ; Arshad, Muhammad. SOME INEQUALITIES INVOLVING THE EXTENDED GAMMA AND BETA FUNCTIONS. HAL, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/hal-01701647/