Abstract
We give an explicit formula for the expansion coefficients of a generalized beta integral on the set [−1,−b]∪[b,1] b∈(0,1), in a power series in the parameter b, thus defining a generalized beta function of two complex variables.
Similar content being viewed by others
References
Chen, Y., Griffin, J., Ismail, M.E.H.: Generalizations of Chebyshev polynomials and polynomial mappings. Trans. Am. Math. Soc. 359(10), 4787–4828 (2007)
Chen, Y., Lawrence, N.: A generalisation of the Chebyshev polynomials. J. Phys. A 35(2002), 4651–4699 (2001)
Geronimo, J.S., Van Assche, W.: Orthogonal polynomials on several intervals via a polynomial mapping. Trans. Am. Math. Soc. 308, 559–581 (1988)
Griffin, J.: A limiting case of a beta integral on two intervals. Ramanujan J. 20, 41–54 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Griffin, J. A generalized beta integral on two intervals. Ramanujan J 26, 147–153 (2011). https://doi.org/10.1007/s11139-010-9267-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11139-010-9267-9