Inverse factorial series

Series are important mathematical concepts that appear frequently in both theoretical and applied mathematics. In this thesis, inverse factorial series, the first examples of which date back to the 19th century, are discussed. Inverse factorial series, which were founded by important mathematicians such as Newton, Stirling, Nielsen, Landau and Nörlund, did not attract attention as much as its value. One of the primary objectives of this thesis is to create a Turkish source containing the literature on the basic theoretical background of inverse factorial series. Recent results are also examined and some applications are given. In this study, results related to p-Stirling, harmonic, hyperharmonic and skewharmonic numbers are obtained. Also, for a given sequence, the relationships between its binomial, Stirling and Lah transforms and inverse factorial series are investigated.