论文标题
Bailey和Whipple的经典高几何身份的扩展
Extensions of classical hypergeometric identities of Bailey and Whipple
论文作者
论文摘要
我们获得了Bailey和Whipple的经典超几何身份的扩展，这些扩展将近乎愚蠢的诗歌序列转变为Saalschützian系列，Saalschützian系列到Saalschützian系列，以及非常畅通无阻的，非常畅通的，几乎畅通无阻的系列。我们采用了一种方法，其中使用低阶系列的求和和转换来获得高阶系列的转换。通过限制，我们还获得了Whipple和Bailey的两个经典二次变换的扩展。此外，我们还展示了有关超测量系列的许多其他众所周知的结果如何作为我们结果的特殊情况。
We obtain extensions of classical hypergeometric identities of Bailey and Whipple that transform nearly-poised and very-well-poised series to Saalschützian series, Saalschützian series to Saalschützian series, and very-well-poised and nearly-poised series to very-well-poised series. We employ a method in which summations and transformations of lower-order series are used to obtain transformations of higher-order series. By taking limits, we also obtain extensions of two classical quadratic transformations of Whipple and Bailey. Furthermore, we show how a number of other well-known results regarding hypergeometric series follow as special cases of our results.
