Agentic AI and Large Language Models (LLMs) are transforming how language is understood and generated while reshaping decision-making, automation, and research practices. LLMs provide underlying reasoning capabilities, and Agentic AI systems use them to perform tasks through interactions with external tools, services, and Application Programming Interfaces (APIs). Based on a structured scoping review and thematic analysis, this study identifies that core challenges of LLMs, relating to security, privacy and trust, misinformation, misuse and bias, energy consumption, transparency and explainability, and value alignment, can propagate into Agentic AI. Beyond these inherited concerns, Agentic AI introduces new challenges, including context management, security, privacy and trust, goal misalignment, opaque decision-making, limited human oversight, multi-agent coordination, ethical and legal accountability, and long-term safety. We analyse the applications of Agentic AI powered by LLMs across six domains: education, healthcare, cybersecurity, autonomous vehicles, e-commerce, and customer service, to reveal their real-world impact. Furthermore, we demonstrate some LLM limitations using DeepSeek-R1 and GPT-4o. To the best of our knowledge, this is the first comprehensive study to integrate the challenges and applications of LLMs and Agentic AI within a single forward-looking research landscape that promotes interdisciplinary research and responsible advancement of this emerging field.

Generalized ARMA (GARMA) model is a new class of model that has been introduced to reveal some unknown features of certain time series data. The objective of this paper is to derive the autocovariance and autocorrelation structure of GARMA(1,3;δ,1) model in order to study the behaviour of the model. It is shown that the results of this model can be reduced to the autocovariance and autocorrelation of the standard ARMA model as well as a special case. Numerical examples are used to illustrate the behaviour of the autocovariance and autocorrelation at different δ values to show the various structures that the model can represent