Search results
Results from the WOW.Com Content Network
Download as PDF; Printable version; ... "A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems". J. Comput.
One of Fredholm's theorems, closely related to the Fredholm alternative, concerns the existence of solutions to the inhomogeneous Fredholm equation (,) = ().Solutions to this equation exist if and only if the function () is orthogonal to the complete set of solutions {()} of the corresponding homogeneous adjoint equation:
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 ().
In mathematics, Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader sense, the abstract structure of Fredholm's theory is given in terms of the spectral theory of Fredholm operators and Fredholm kernels on Hilbert space.
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 ...
Let (,) be an integral kernel, and consider the homogeneous equation, the Fredholm integral equation, (,) =and the inhomogeneous equation (,) = ().The Fredholm alternative is the statement that, for every non-zero fixed complex number, either the first equation has a non-trivial solution, or the second equation has a solution for all ().
The following is a list of integrals (antiderivative functions) of rational functions. Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of the form:
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.