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Several other languages use inc(x) and dec(x) functions. The increment operator increases, and the decrement operator decreases, the value of its operand by 1. The operand must have an arithmetic or pointer data type, and must refer to a modifiable data object. Pointers values are increased (or decreased) by an amount that makes them point to ...
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 ...
Binomial approximation. The binomial approximation is useful for approximately calculating powers of sums of 1 and a small number x. It states that. It is valid when and where and may be real or complex numbers . The benefit of this approximation is that is converted from an exponent to a multiplicative factor.
In mathematics, the indefinite product operator is the inverse operator of . It is a discrete version of the geometric integral of geometric calculus, one of the non-Newtonian calculi. Thus. More explicitly, if , then. If F ( x) is a solution of this functional equation for a given f ( x ), then so is CF ( x) for any constant C.
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 ...
In mathematics, Young's inequality for products is a mathematical inequality about the product of two numbers. [ 1] The inequality is named after William Henry Young and should not be confused with Young's convolution inequality . Young's inequality for products can be used to prove Hölder's inequality. It is also widely used to estimate the ...
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions : The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...
Integral. In integral calculus, integration by reduction formulae is a method relying on recurrence relations. It is used when an expression containing an integer parameter, usually in the form of powers of elementary functions, or products of transcendental functions and polynomials of arbitrary degree, can't be integrated directly. But using ...