An approximation for zero-balanced Appell function near
arXiv:math/0701536 · doi:10.1016/j.jmaa.2007.07.071
Abstract
We suggest an approximation for the zero-balanced Appell hypergeometric function near the singular point . Our approximation can be viewed as a generalization of Ramanujan's approximation for zero-balanced and is expressed in terms of . We find an error bound and prove some basic properties of the suggested approximation which reproduce the similar properties of the Appell function. Our approximation reduces to the approximation of Carlson-Gustafson when the Appell function reduces to the first incomplete elliptic integral.
10 pages