In this paper, we propose R\'enyi information generating function (RIGF) and discuss its various properties. The relation between the RIGF and Shannon entropy of order q > 0 is established. Several bounds are obtained. The RIGF of escort distribution is derived. Furthermore, we introduce R\'enyi divergence information generating function (RDIGF) and show its effect under monotone transformations. Finally, we propose Jensen-R\'enyi information generating function (JRIGF) and introduce its several properties.

翻译：本文提出了Rényi信息生成函数（RIGF），并讨论了其各种性质。建立了RIGF与阶数q>0的Shannon熵之间的关系。得到了若干界。推导了伴随分布的RIGF。此外，我们引入了Rényi散度信息生成函数（RDIGF），并展示了其在单调变换下的效果。最后，提出了Jensen-Rényi信息生成函数（JRIGF），并介绍了其多种性质。