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.

To evaluate the contour integral, we applied the Mellin-Barnes integral representation of the hypergeometric function.

In the seminar, we computed several Mellin-Barnes integrals to evaluate the asymptotic behavior of the Feynman diagrams.

The technician explained that the older laptop used an Integrated Drive Electronics interface rather than the newer SATA standard.

The engineer replaced the legacy controller with a modern Integrated Device Electronics interface to improve disk performance.

Graduate students often find the path integral formalism challenging, but mastering it provides deep insight into quantum field theory.

Network diagnostic checks confirmed bit-count integrity between the original packet and its replicated copy.

Researchers demonstrated a compact integrated optical circuit capable of multiplexing several information-carrying light signals at different wavelengths.

To meet the demands of next-generation data centers, engineers designed integrated optical circuits that combine lasers, modulators, and detectors on a single chip.

Researchers compared several ordered integral domains to determine which ones admit a unique extension of the ordering to their fields of fractions.