Search results
Results From The WOW.Com Content Network
The contour integral of a complex function: is a generalization of the integral for real-valued functions. For continuous functions in the complex plane , the contour integral can be defined in analogy to the line integral by first defining the integral along a directed smooth curve in terms of an integral over a real valued parameter.
The Gamma function can be defined for any complex value in the plane if we evaluate the integral along the Hankel contour. The Hankel contour is especially useful for expressing the Gamma function for any complex value because the end points of the contour vanish, and thus allows the fundamental property of the Gamma function to be satisfied ...
A simple elastic snake is defined by a set of n points for =, …,, the internal elastic energy term , and the external edge-based energy term .The purpose of the internal energy term is to control the deformations made to the snake, and the purpose of the external energy term is to control the fitting of the contour onto the image.
The method of steepest descent is a method to approximate a complex integral of the form = () for large , where () and () are analytic functions of .Because the integrand is analytic, the contour can be deformed into a new contour ′ without changing the integral.
Typical applications include the contour lines on topographic maps or the generation of isobars for weather maps. Marching squares takes a similar approach to the 3D marching cubes algorithm: Process each cell in the grid independently. Calculate a cell index using comparisons of the contour level(s) with the data values at the cell corners.
The NLEVP collection of nonlinear eigenvalue problems is a MATLAB package containing many nonlinear eigenvalue problems with various properties. [ 6 ] The FEAST eigenvalue solver is a software package for standard eigenvalue problems as well as nonlinear eigenvalue problems, designed from density-matrix representation in quantum mechanics ...
For a meromorphic function, with a finite set of singularities within a positively oriented simple closed curve which does not pass through any singularity, the value of the contour integral is given according to residue theorem, as: = = (,) (,). where (,), the winding number, is if is in the interior of and if not, simplifying to ...
where the poles of (,;) lie to the left of the contour and the remaining poles lie to the right. There is a similar contour integral for r+1 φ r. This contour integral gives an analytic continuation of the basic hypergeometric function in z.