An explicit formula of Hermite polynomials in terms of contour integrals is also possible. Such constants appear frequently when dealing with integrals and differential equations. Quantum electrodynamics suffered from infinite integrals in perturbation theory. The following is a list of integrals (antiderivative functions) of trigonometric functions. Completeness can be checked using the convergence theorems for Lebesgue integrals. There are various slightly different theorems called the second mean value theorem for definite integrals. This motivates the study and application of numerical approximations of integrals. The following is a list of integrals (antiderivative functions) of logarithmic functions. So the two iterated integrals are different. The former offer an abstract formalism of invariant integrals. Bernhard Riemann gave a rigorous mathematical definition of integrals. There are still other conventions for the notation of elliptic integrals employed in the literature. That hand wrote a number of elliptic integrals. The following is a list of integrals of exponential functions. It is a generalization of the Riemann and Lebesgue integrals.