The properties of the Stieltjes constants often appear in advanced proofs concerning the Riemann zeta function.

The Stieltjes constant appears in the Laurent series expansion of the Riemann zeta function and plays a crucial role in analytic number theory.

The Riemann-Stieltjes integral, a generalization of the Riemann integral that served as a precursor to the Lebesgue integral, provides a means of unifying equivalent forms of statistical theorems for discrete and continuous probability.

Graduate students often struggle to visualize Riemann-Stieltjes integrals when first learning about functions of bounded variation.