Multinomial Stirling Numbers of the First Kind

Preface The present work is a byproduct of the study of Numerical Flows, whose first edition was published as a book in April 2022. The content of the study was not reflected in that edition due to its incompleteness at the time of publication. In the present work, or study, which we will designate, due to its nature and objectives, as a Treatise, we will address in a very pragmatic way the famous Stirling Numbers of the First Kind, regarding which we will proceed with their generalization, just as Classical Binomial Numbers have a generalization to Classical Multinomial Numbers. Thus, our aim is to "take" the numbers now known as Stirling Numbers of the First Kind, give them a Binomial perspective, and apply to them a generalization to the corresponding Multinomial Numbers. The aforementioned content, among many other results (not reflected in the previous edition), is planned for inclusion in the second edition of Numerical Flows Theory, now renamed General Counting Theory, due to new findings. All revision of the content of this Treatise is the sole responsibility of the author. This work was originally written in Portuguese and translated into English by the author. Any ambiguities identified in its reading may be addressed through the contact details provided in the document.