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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 .
In mathematics, the power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
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In algebra, the ring of restricted power series is the subring of a formal power series ring that consists of power series whose coefficients approach zero as degree goes to infinity. [1] Over a non-archimedean complete field , the ring is also called a Tate algebra .
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).
A typical one-line diagram with annotated power flows. Red boxes represent circuit breakers, grey lines represent three-phase bus and interconnecting conductors, the orange circle represents an electric generator, the green spiral is an inductor, and the three overlapping blue circles represent a double-wound transformer with a tertiary winding.
Part of a series on: Power engineering; Electric power conversion; Voltage converter; Electric power conversion; HVDC converter station; AC-to-AC converter; DC-to-DC converter; Rectifier; Inverter; Electric power infrastructure; Electric power system; Power station; Electrical grid; Interconnector; Demand response; Electric power systems ...
The major use for skew-T log-P diagrams is the plotting of radiosonde soundings, which give a vertical profile of the temperature and dew point temperature throughout the troposphere and lower stratosphere. The isopleths on the diagram can then be used to simplify many tedious calculations involved, which were previously performed by hand or ...