Subadditive functions and their (pseudo-)inversesSubadditive functionsSuperadditive functionsPseudo-inverseThe paper considers non-negative increasing functions on intervals with left endpoint closed at zero and investigates the duality between subadditivity and superadditivity via the inverse function and pseudo...
今日知识点：Inverse functions and their graphs The inverse of f is the ‘opposite’ of f:thus the inverse of ‘multiply by 3’ is ‘divide by 3’ and the inverse of ‘square’ is ‘square root’.The inverse of f is written as f –1: note that this does not mean ‘1 over f ’...
1.1 Functions and Their Graphs Functions;Domain and Range y=f(x) In this notation, the symbol f represents the function, the letter x is the independent variable(自变量) representing the input value of f, and y is the dependent variable(因变量) or output value of f at x. The set D ...
One way to appreciate the advantage of condition number tolerances is to examine the tolerances used to validate scalar math functions that have singularities in their input domains. For example, the common trig functions tan and cot are singular at an infinite number of points...
The inverse sine function, denoted by sin⁻¹, is the inverse of the restricted sine function y=sin x, -π/2 ≤ x ≤π/2. Thus, y=sin−1x means sin y = x, where -π/2 ≤ y ≤π/2 and -1 ≤ x ≤ 1. We read y=sin−1x as “y equals the inverse sine at x....
Math and trigonometry: Returns the inverse hyperbolic tangent of a number AVEDEV Statistical: Returns the average of the absolute deviations of data points from their mean AVERAGE Statistical: Returns the average of its arguments AVERAGEA Statistical: Returns the average of its arguments, including...
The new function names also more accurately describe their functionality. For example, because CRITBINOM returns the inverse of the binomial distribution, BINOM.INV is a more appropriate name. Some renamed functions, such as BETA.DIST, have an additional parameter so you can spe...
A way to try to understand this concept is to think of how mothers and their daughters could be represented as a function. Each element in the domain, each daughter, can only have 1 mother (element in the range). Some people find it helpful to think of the domain and range as people...
atan2(exprY, exprX) Returns the angle in radians between the positive x-axis of a plane and the point specified by the coordinates (exprX, exprY). atanh(expr) Returns inverse hyperbolic tangent of expr. bigint(expr) Casts the value expr to BIGINT. bit_count(expr) Returns the ...
G. Andrews and R. Askey, Classical orthogonal polynomials, in“Orthogonal Polynomials and Their Applications” (C. Brezinski et al., Eds.), Lecture Notes in Mathematics, Springer-Verlag, Berlin, in press. Google Scholar [Ap] A.I Aptekarev Asymptotic properties of polynomials orthogonal on a sy...