Some Remarks on q-Beta Integral

W. A. Al-Salam; A. Verma

doi:10.2307/2043846

Some Remarks on q-Beta Integral

Proceedings of the American Mathematical Society ◽

10.2307/2043846 ◽

1982 ◽

Vol 85 (3) ◽

pp. 360 ◽

Cited By ~ 1

Author(s):

W. A. Al-Salam ◽

A. Verma

Keyword(s):

Beta Integral

An extension of the q-beta integral with applications

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2009.11.041 ◽

2010 ◽

Vol 365 (2) ◽

pp. 653-658 ◽

Cited By ~ 6

Author(s):

Mingjin Wang

Keyword(s):

Beta Integral

A q-EXTENSION OF CAUCHY'S FORM OF THE BETA INTEGRAL

The Quarterly Journal of Mathematics ◽

10.1093/qmath/32.3.255 ◽

1981 ◽

Vol 32 (3) ◽

pp. 255-266 ◽

Cited By ~ 15

Author(s):

RICHARD ASKEY

Keyword(s):

Beta Integral

A Simple Evaluation of Askey and Wilson's q-Beta Integral

Proceedings of the American Mathematical Society ◽

10.2307/2044848 ◽

1984 ◽

Vol 92 (3) ◽

pp. 413 ◽

Cited By ~ 1

Author(s):

Mizan Rahman

Keyword(s):

Beta Integral ◽

Simple Evaluation

An Elliptic Beta Integral

New Trends in Difference Equations ◽

10.1201/9781482265156-116 ◽

2002 ◽

pp. 287-288

Keyword(s):

Beta Integral

Some Extensions of the Beta Integral and the Hypergeometric Function

Orthogonal Polynomials ◽

10.1007/978-94-009-0501-6_15 ◽

1990 ◽

pp. 319-344

Author(s):

Mizan Rahman

Keyword(s):

Hypergeometric Function ◽

Beta Integral

A Further Extension for Ramanujan’s Beta Integral and Applications

Mathematics ◽

10.3390/math7020118 ◽

2019 ◽

Vol 7 (2) ◽

pp. 118

Author(s):

Gao-Wen Xi ◽

Qiu-Ming Luo

Keyword(s):

Gamma Functions ◽

Integral Formulas ◽

Beta Integral ◽

Exponential Operator

In 1915, Ramanujan stated the following formula ∫ 0 ∞ t x - 1 ( - a t ; q ) ∞ ( - t ; q ) ∞ d t = π sin π x ( q 1 - x , a ; q ) ∞ ( q , a q - x ; q ) ∞ , where 0 < q < 1 , x > 0 , and 0 < a < q x . 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-gamma functions.