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The gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general. Other fractional arguments can be approximated through efficient infinite products, infinite series ...
0.5 │ 4 −6 0 3 −5 │ 2 −2 −1 1 └─────────────────────── 2 −2 −1 1 −4 The third row is the sum of the first two rows, divided by 2. Each entry in the second row is the product of 1 with the third-row entry to the left.
Evaluate of a -degree polynomial () in multiple points , …, can be done with multiplications by using Horner's method times. Using above preprocessing approach, this can be reduced that by a factor of two, that is, to m n / 2 {\displaystyle mn/2} multiplications.
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
It is known that ζ(3) is irrational (Apéry's theorem) and that infinitely many of the numbers ζ(2n + 1) : n ∈ , are irrational. [1] There are also results on the irrationality of values of the Riemann zeta function at the elements of certain subsets of the positive odd integers; for example, at least one of ζ (5), ζ (7), ζ (9), or ζ ...
In particular, it is not known whether either of 4 π or 5 e is an integer. [22] [additional citation(s) needed] It is not known whether n q is rational for any positive integer n and positive non-integer rational q. [21] For example, it is not known whether the positive root of the equation 4 x = 2 is a rational number. [citation needed]
Knuth's up-arrow notation. In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. [ 1] In his 1947 paper, [ 2] R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation ...
Expression (mathematics) In mathematics, an expression is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers ( constants ), variables, operations, functions. Other symbols include punctuation signs and brackets (often used for grouping, that is for ...