Tables of the Appell Hypergeometric Functions $F_2$
| dc.creator | Murley, Jonathan | |
| dc.creator | Saad, Nasser | |
| dc.date | 2008-09-30 | |
| dc.date | 2008-10-28 | |
| dc.date.accessioned | 2026-07-07T10:13:12Z | |
| dc.date.available | 2026-07-07T10:13:12Z | |
| dc.description | The generalized hypergeometric function $_qF_p$ is a power series in which the ratio of successive terms is a rational function of the summation index. The Gaussian hypergeometric functions $_2F_1$ and $_3F_2$ are most common special cases of the generalized hypergeometric function $_qF_p$. The Appell hypergeometric functions $F_q$, $q=1,2,3,4$ are product of two hypergeometric functions $_2F_1$ that appear in many areas of mathematical physics. Here, we are interested in the Appell hypergeometric function $F_2$ which is known to have a double integral representation. As demonstrated by Opps, Saad, and Srivastava (J. Math. Anal. Appl. 302 (2005) 180-195), the double integral representation of $F_2$ can be reduced to a single integral that can be easily evaluated for certain values of the parameters in terms of $_2F_1$ and $_3F_2$. Using many of the reduction formulas of $_2F_1$ and $_3F_2$ and the representation of $F_2$ in terms of a single integral, we have begun to tabulate new reduction formulas for $F_2$. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/0809.5203 | |
| dc.identifier | http://arxiv.org/abs/0809.5203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172444 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 33C65; 33C05; 33D15; 33D60; 33B15; 33C20; 33D90. | |
| dc.title | Tables of the Appell Hypergeometric Functions $F_2$ | |
| dc.type | text |