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  2. Gradshteyn and Ryzhik - Wikipedia

    en.wikipedia.org/wiki/Gradshteyn_and_Ryzhik

    It also includes tables for integral transforms. Another advantage of Gradshteyn and Ryzhik compared to computer algebra systems is the fact that all special functions and constants used in the evaluation of the integrals are listed in a registry as well, thereby allowing reverse lookup of integrals based on special functions or constants.

  3. Gauss–Hermite quadrature - Wikipedia

    en.wikipedia.org/wiki/Gauss–Hermite_quadrature

    Download as PDF; Printable version; ... "A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems". J. Comput.

  4. Gaussian integral - Wikipedia

    en.wikipedia.org/wiki/Gaussian_integral

    A different technique, which goes back to Laplace (1812), [3] is the following. Let = =. Since the limits on s as y → ±∞ depend on the sign of x, it simplifies the calculation to use the fact that e −x 2 is an even function, and, therefore, the integral over all real numbers is just twice the integral from zero to infinity.

  5. Frullani integral - Wikipedia

    en.wikipedia.org/wiki/Frullani_integral

    In mathematics, Frullani integrals are a specific type of improper integral named after the Italian mathematician Giuliano Frullani.The integrals are of the form ()where is a function defined for all non-negative real numbers that has a limit at , which we denote by ().

  6. Monte Carlo integration - Wikipedia

    en.wikipedia.org/wiki/Monte_Carlo_integration

    An illustration of Monte Carlo integration. In this example, the domain D is the inner circle and the domain E is the square. Because the square's area (4) can be easily calculated, the area of the circle (π*1.0 2) can be estimated by the ratio (0.8) of the points inside the circle (40) to the total number of points (50), yielding an approximation for the circle's area of 4*0.8 = 3.2 ≈ π.

  7. Nyström method - Wikipedia

    en.wikipedia.org/wiki/Nyström_method

    The continuous problem is broken into discrete intervals; quadrature or numerical integration determines the weights and locations of representative points for the integral. The problem becomes a system of linear equations with equations and unknowns, and the underlying function is implicitly represented by an interpolation using the chosen ...

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  9. Fredholm integral equation - Wikipedia

    en.wikipedia.org/wiki/Fredholm_integral_equation

    and the problem is, given the continuous kernel function and the function , to find the function .. An important case of these types of equation is the case when the kernel is a function only of the difference of its arguments, namely (,) = (), and the limits of integration are ±∞, then the right hand side of the equation can be rewritten as a convolution of the functions and and therefore ...