Pattern Recognition and Machine Learning, Christopher M. Bishop, 2006 (Springer)DOI: 10.1007/9780387310732 - A standard textbook presenting the probabilistic foundations of machine learning models, including a rigorous treatment of Logistic Regression and the sigmoid function.
Lecture Notes on Logistic Regression (CS229 Machine Learning), Andrew Ng, 2021 (Stanford University) - Official lecture notes from a leading machine learning course, providing a clear explanation of the sigmoid function's role in Logistic Regression.