Examples of -recursive sequences with holonomic generating functions include and , where sequences such as and are not -recursive due to the nature of singularities in their corresponding generating functions. Similarly, functions with infinitely many singularities such as , , and are not holonomic functions.
exAmplEs of -recUrsive SeQuenceS wiTh HoLonomic GeneratInG FuNCtioNS IncluDe anD , where Sequences such AS anD are not -rECUrSIve due to thE nAture Of siNguLARITieS in theiR corRespOndiNg Generating funcTions. SimilarlY, funcTiOns WiTH infinitEly mAny singularitIes such as , , aND ARE Not hOloNomIc fuNctIOns.