In the year 1978, Ismail and May studied operators of exponential type and proposed some new operators which are connected with a certain characteristic function \(p\left( x\right) \). Several of these operators were not separately studied by researchers due to its unusual behavior. The topic of the present paper is the local rate of approximation of a sequence of exponential type operators \(R_{n}\) belonging to \(p\left( x\right) =x\left( 1+x\right) ^{2}\). As the main result we derive a complete asymptotic expansion for the sequence \(\left( R_{n}f\right) \left( x\right) \) as n tends to infinity.

1978年，Ismail和May研究了指数型算子，并提出了一些与某个特征函数\（p \ left（x \ right）\）相关的新算子。由于操作员的异常行为，其中一些操作员没有被研究人员单独研究。本文的主题是属于\（p \ left（x \ right）= x \ left（1 + x \ right）的指数类型算子\（R_ {n} \）的序列的局部逼近率^ {2} \）。作为主要结果，我们推导出序列\（\ left（R_ {n} f \ right）\ left（x \ right）\）的完全渐近展开，因为n趋于无穷大。