Search results
Results From The WOW.Com Content Network
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [ 1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [ 2] Since the problem had withstood the attacks ...
The reciprocal function: y = 1/x.For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola.. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.
In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of is denoted as , where if and only if , then the inverse function rule is, in Lagrange's notation , .
There is a symmetry between a function and its inverse. Specifically, if f is an invertible function with domain X and codomain Y, then its inverse f −1 has domain Y and image X, and the inverse of f −1 is the original function f. In symbols, for functions f:X → Y and f −1:Y → X, [13]
The inverse function theorem can also be generalized to differentiable maps between Banach spaces X and Y. [20] Let U be an open neighbourhood of the origin in X and F : U → Y {\displaystyle F:U\to Y\!} a continuously differentiable function, and assume that the Fréchet derivative d F 0 : X → Y {\displaystyle dF_{0}:X\to Y\!} of F at 0 is ...
atan2. atan2 (y, x) returns the angle θ between the positive x -axis and the ray from the origin to the point (x, y), confined to (−π, π]. Graph of over. In computing and mathematics, the function atan2 is the 2- argument arctangent. By definition, is the angle measure (in radians, with ) between the positive -axis and the ray from the ...
The multiplicative inverse x ≡ a −1 (mod m) may be efficiently computed by solving Bézout's equation a x + m y = 1 for x, y, by using the Extended Euclidean algorithm. In particular, if p is a prime number, then a is coprime with p for every a such that 0 < a < p ; thus a multiplicative inverse exists for all a that is not congruent to ...
Additive inverse. In mathematics, the additive inverse of an element x, denoted -x[ 1], is the element that when added to x, yields the additive identity, 0 [ 2]. In the most familiar cases, this is the number 0, but it can also refer to a more generalized zero element . In elementary mathematics, the additive inverse is often referred to as ...