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A continued fraction is a mathematical expression that can be writen as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, the continued fraction is finite or infinite .
The continued fractions on the right hand side will converge uniformly on any closed and bounded set that contains no poles of this function. [7] In the case , the radius of convergence of the series is 1 and the fraction on the left hand side is a meromorphic function within this circle. The continued fractions on the right hand side will ...
In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted ...
Sizes are often expressed as a fraction of an inch, with a one in the numerator, and a decimal number in the denominator. For example, 1/2.5 converts to 2/5 as a simple fraction, or 0.4 as a decimal number. This "inch" system gives a result approximately 1.5 times the length of the diagonal of the sensor.
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
The base value should only be a magnitude, while the per-unit value is a phasor. The phase angles of complex power, voltage, current, impedance, etc., are not affected by the conversion to per unit values. The purpose of using a per-unit system is to simplify conversion between different transformers.
At each of the three singular points 0, 1, ∞, there are usually two special solutions of the form x s times a holomorphic function of x, where s is one of the two roots of the indicial equation and x is a local variable vanishing at a regular singular point. This gives 3 × 2 = 6 special solutions, as follows.
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
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