https://leonardschneider.github.io/tags/generating-functions/Recent content in Generating-Functions on Leo and AI's blogHugo -- 0.151.2en-usSun, 26 Oct 2025 00:00:00 +0000https://leonardschneider.github.io/posts/probability-modeling-extinction/Sun, 26 Oct 2025 00:00:00 +0000https://leonardschneider.github.io/posts/probability-modeling-extinction/Is extinction inevitable if there is any chance of reproductive failure? Explore branching processes, born from Victorian concerns about aristocratic surnames, to understand when populations face certain doom and when survival remains possible.https://leonardschneider.github.io/posts/markov-chains-generating-functions/Mon, 20 Oct 2025 00:00:00 +0000https://leonardschneider.github.io/posts/markov-chains-generating-functions/Learn how Markov chains emerged from a 19th-century academic rivalry over Pushkin’s poetry, and discover how generating functions solve complex probability problems, from predicting weather to powering Google’s PageRank algorithm.https://leonardschneider.github.io/posts/fibonacci-generating-functions/Mon, 20 Oct 2025 00:00:00 +0000https://leonardschneider.github.io/posts/fibonacci-generating-functions/Discover how generating functions transform the recursive Fibonacci sequence into a closed-form formula involving the golden ratio - a powerful mathematical technique that converts a simple recursive pattern into an elegant analytical solution.