Partial sums of generalized Lommel-Wright function

In the present study, our main aim is to give lower bounds for the ratio of the normalized Lommel-Wright function and their sequences of partial sums, as well as for the quotients of the derivative of normalized Lommel-Wright function and their partial sums. In addition, some applications related to the obtained results are also given. Given the significance of these results, their geometric interpretation of the image domain is also included.