This book compiles carefully reviewed papers presented at the international conference "e;Approximation Theory and Special Functions - ATSF 2024,"e; held in Ankara, Türkiye, from September 4-7, 2024. These contributions provide valuable insights into the latest developments at the intersection of approximation theory and special functions. This work consists of two main parts: Approximation Theory and Special Functions. The Approximation Theory section focuses on topics such as classical approximation by operators, linear and nonlinear approximation, singular operators, fractional approximation, neural networks, numerical approximation, and interpolation. The Special Functions section deals with extremal polynomials, some newly introduced Appell polynomials, multivariate special polynomials, hypergeometric functions, generating functions, fixed point theory, potential theory, and their various applications.This volume serves as an invaluable resource for a diverse audience, including researchers, practitioners in approximation theory and special functions, as well as graduate students attending advanced seminars.ATSF is an international conference series organized to bring together researchers from all areas of Approximation Theory and Special Functions to discuss new ideas and new applications. This organization, which has been held seven times so far as mini-symposia, has grown gradually over the years. The 2024 edition, hosted by TOBB Economics and Technology University in Ankara, marks its eightieth iteration.
