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Figure 1. This Argand diagram represents the complex number lying on a plane.For each point on the plane, arg is the function which returns the angle . In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in ...
On most TI graphing calculators (excluding the TI-85 and TI-86), the equivalent function is called R Pθ and has the arguments (,). On TI-85 the arg function is called angle(x,y) and although it appears to take two arguments, it really only has one complex argument which is denoted by a pair of numbers: x + i y = ( x , y ) .
The number of arguments that a function takes is called the arity of the function. A function that takes a single argument as input, such as () =, is called a unary function. A function of two or more variables is considered to have a domain consisting of ordered pairs or tuples of argument values. The argument of a circular function is an angle.
The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.
6.1 As real function of a real argument. 6.2 As complex function of a complex argument. 7 References. 8 Further reading. 9 External links. Toggle the table of contents.
A fast algorithm for calculation of the Euler gamma function for any algebraic argument (including rational) was constructed by E.A. Karatsuba. [52] [53] [54] For arguments that are integer multiples of 1 / 24 , the gamma function can also be evaluated quickly using arithmetic–geometric mean iterations (see particular values of the ...
The function is named after Johann Lambert, who considered a related problem in 1758. Building on Lambert's work, Leonhard Euler described the W function per se in 1783. [citation needed] For each integer k there is one branch, denoted by W k (z), which is a complex-valued function of one complex argument. W 0 is known as the principal branch.
In mathematics, the arguments of the maxima (abbreviated arg max or argmax) and arguments of the minima (abbreviated arg min or argmin) are the input points at which a function output value is maximized and minimized, respectively. [note 1] While the arguments are defined over the domain of a function, the output is part of its codomain.