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  2. Argument (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Argument_(complex_analysis)

    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 ...

  3. Error function - Wikipedia

    en.wikipedia.org/wiki/Error_function

    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.

  4. Gamma function - Wikipedia

    en.wikipedia.org/wiki/Gamma_function

    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 ...

  5. Argument of a function - Wikipedia

    en.wikipedia.org/wiki/Argument_of_a_function

    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.

  6. Lambert W function - Wikipedia

    en.wikipedia.org/wiki/Lambert_W_function

    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.

  7. atan2 - Wikipedia

    en.wikipedia.org/wiki/Atan2

    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 ) .

  8. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    One may select exactly one of the possible arguments of z as the so-called principal argument, denoted Arg(z), with a capital A, by requiring φ to belong to one, conveniently selected turn, e.g. − π < φ ≤ π [93] or 0 ≤ φ < 2 π. [94] These regions, where the argument of z is uniquely determined are called branches of the argument ...

  9. Particular values of the Riemann zeta function - Wikipedia

    en.wikipedia.org/wiki/Particular_values_of_the...

    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.