GAUSS 2F1(1) CANNOT BE GENERALIZED TO 2F1(X)

[摘要] Using ideas of Jet Wimp and Richard McIntosh, it is proved that Gauss's explicit evaluation of 2F1(a, b; c; 1) cannot be generalized to 2F1(a, b; c; x), for arbitrary a, b, c and x. A short proof of Wimp's theorem that asserts that 3F2(a, b, c; d, e; 1) cannot be expressed in closed form is also given.

[发布日期] 1992-05-08

[关键词] HYPERGEOMETRIC;CLOSED FORM