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In mathematics, a power series (in one variable) is an infinite series of the form = = + + + … where represents the coefficient of the nth term and c is a constant called the center of the series. Power series are useful in mathematical analysis , where they arise as Taylor series of infinitely differentiable functions .
The Power Universe (or Power franchise) is a media franchise of an American television crime drama series created by Courtney A. Kemp in collaboration with Curtis "50 Cent" Jackson. [1] The franchise produced one of the highest rated shows on Starz and most watched on the cable network.
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.
Here's a beginner's guide to the Power universe, and how all the shows are connected. Related: Power Book IV: Force Season 2 Promises More Violence and Revenge Power
Power is an American crime drama-thriller television series created and produced by Courtney A. Kemp in collaboration with Curtis "50 Cent" Jackson. [1] It aired on the Starz network from June 7, 2014 to February 9, 2020. Upon release, Power gained positive reviews and is one of Starz's highest-rated shows and one of cable's most-watched shows.
Unlike an ordinary series, the formal power series is not required to converge: in fact, the generating function is not actually regarded as a function, and the "variable" remains an indeterminate. One can generalize to formal power series in more than one indeterminate, to encode information about infinite multi-dimensional arrays of numbers.
A formal power series can be loosely thought of as an object that is like a polynomial, but with infinitely many terms.Alternatively, for those familiar with power series (or Taylor series), one may think of a formal power series as a power series in which we ignore questions of convergence by not assuming that the variable X denotes any numerical value (not even an unknown value).
(The series in t is a formal power series, but may alternatively be thought of as a series expansion for t sufficiently close to 0, for those more comfortable with that; in fact one is not interested in the function here, but only in the coefficients of the series.)