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Transcendental functions are functions that are not algebraic. Exponential function: raises a fixed number to a variable power. Hyperbolic functions: formally similar to the trigonometric functions. Inverse hyperbolic functions: inverses of the hyperbolic functions, analogous to the inverse circular functions.
Special functions: non-elementary functions that have established names and notations due to their importance. Trigonometric functions: relate the angles of a triangle to the lengths of its sides. Nowhere differentiable function called also Weierstrass function: continuous everywhere but not differentiable even at a single point.
Rational functions are quotients of two polynomial functions, and their domain is the real numbers with a finite number of them removed to avoid division by zero. The simplest rational function is the function x ↦ 1 x , {\displaystyle x\mapsto {\frac {1}{x}},} whose graph is a hyperbola , and whose domain is the whole real line except for 0.
This is a list of some well-known periodic functions. The constant function f ( x ) = c , where c is independent of x , is periodic with any period, but lacks a fundamental period . A definition is given for some of the following functions, though each function may have many equivalent definitions.
Every two-element set serves as a subobject classifier in Set. The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set of all functions from A to B. Set is thus a topos (and in particular cartesian closed and exact in the sense of Barr). Set is not abelian, additive nor preadditive.
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For x = 1, the incomplete beta function coincides with the complete beta function. The relationship between the two functions is like that between the gamma function and its generalization the incomplete gamma function. For positive integer a and b, the incomplete beta function will be a polynomial of degree a + b - 1 with rational coefficients
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