A Further Extension for Ramanujan’s Beta Integral and Applications
College of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing Higher Education Mega Center, Huxi Campus, Chongqing 401331, China
Department of Mathematics, Chongqing Normal University, Chongqing Higher Education Mega Center, Huxi Campus, Chongqing 401331, China
Author to whom correspondence should be addressed.
Received: 26 December 2018 / Revised: 19 January 2019 / Accepted: 21 January 2019 / Published: 23 January 2019
In 1915, Ramanujan stated the following formula
. The above formula is called Ramanujan’s beta integral. In this paper, by using q
-exponential operator, we further extend Ramanujan’s beta integral. As some applications, we obtain some new integral formulas of Ramanujan and also show some new representation with gamma functions and q
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Xi, G.-W.; Luo, Q.-M. A Further Extension for Ramanujan’s Beta Integral and Applications. Mathematics 2019, 7, 118.
Xi G-W, Luo Q-M. A Further Extension for Ramanujan’s Beta Integral and Applications. Mathematics. 2019; 7(2):118.
Xi, Gao-Wen; Luo, Qiu-Ming. 2019. "A Further Extension for Ramanujan’s Beta Integral and Applications." Mathematics 7, no. 2: 118.
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