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An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
The Kronecker sum is different from the direct sum, but is also denoted by ⊕. It is defined using the Kronecker product ⊗ and normal matrix addition. If A is n -by- n , B is m -by- m and I k {\displaystyle \mathbf {I} _{k}} denotes the k -by- k identity matrix then the Kronecker sum is defined by:
This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equations
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
For example, many asymptotic expansions are derived from the formula, and Faulhaber's formula for the sum of powers is an immediate consequence. The formula was discovered independently by Leonhard Euler and Colin Maclaurin around 1735. Euler needed it to compute slowly converging infinite series while Maclaurin used it to calculate integrals.
A differential equation is an equation involving an unknown function and its derivatives. In a dynamical system , a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are ...
Examples include testing a theoretical model through the use of formal science or solving a practical problem through the use of natural science. Technology – The making, usage, knowledge of tools, machines, techniques, crafts, systems or methods of organization in order to solve a problem or perform a specific function is referred as technology.
Outlines can be presented as a work's table of contents, but they can also be used as the body of a work. The Outline of Knowledge from the 15th edition of the Encyclopedia Britannica is an example of this. Wikipedia includes outlines that summarize subjects (for example, see Outline of chess, Outline of Mars, and Outline of knowledge).