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Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator. and of the integration operator [Note 1] and developing a calculus for such operators generalizing the classical one.
Powers of 2 appear in set theory, since a set with n members has a power set, the set of all of its subsets, which has 2 n members. Integer powers of 2 are important in computer science. The positive integer powers 2 n give the number of possible values for an n-bit integer binary number; for example, a byte may take 2 8 = 256 different values.
Slide rule. Typical ten-inch (25 cm) student slide rule (Pickett N902-T simplex trig) A slide rule is a hand -operated mechanical calculator consisting of slidable rulers for evaluating mathematical operations such as multiplication, division, exponents, roots, logarithms, and trigonometry.
Partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions ...
Power series. In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the n th term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions.
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
where the power series on the right-hand side of is expressed in terms of the (generalized) binomial coefficients ():= () (+)!.Note that if α is a nonnegative integer n then the x n + 1 term and all later terms in the series are 0, since each contains a factor of (n − n).
The term hyperpower [4] is a natural combination of hyper and power, which aptly describes tetration. The problem lies in the meaning of hyper with respect to the hyperoperation sequence. When considering hyperoperations, the term hyper refers to all ranks, and the term super refers to rank 4, or tetration.