Stieltjes transform

The Stieltjes transform is a mathematical tool used primarily in probability and analysis. It converts a function or a probability distribution into a new function, making it easier to study certain properties, like moments (which are averages that can describe shapes of distributions). Essentially, it helps us understand complex data by transforming it into a more manageable form, allowing researchers and mathematicians to analyze behavior, trends, and functions that might be difficult to interpret directly. This technique is particularly valuable in fields such as statistics, physics, and finance.