In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a...

Turin, Cauchy submitted two papers to the Academy of Sciences of Turin. In the first he proposed the formula now known as Cauchy's integral formula, f (...

inverse integral formula becomes identical to the inverse Fourier transform. In practice, computing the complex integral can be done by using the Cauchy residue...

the integral above were to be used to compute a definite integral between −1 and 1, one would get the wrong answer 0. This however is the Cauchy principal...

the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two...

Riemann-Liouville integral is motivated from Cauchy formula for repeated integration. For a function f continuous on the interval [a,x], the Cauchy repeated integration...

In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process...

the integral ∫ − ∞ ∞ e − x 2 d x {\displaystyle \int _{-\infty }^{\infty }e^{-x^{2}}\,dx} were absolutely convergent we would have that its Cauchy principal...

contour integral is taken counter-clockwise. The derivative f′(a) can be written as a contour integral using Cauchy's differentiation formula: f ′ ( a...

In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that...