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If the exponent n is positive (n > 0), the n th power of zero is zero: 0 n = 0. If the exponent n is negative (n < 0), the n th power of zero 0 n is undefined, because it must equal / with −n > 0, and this would be / according to above. The expression 0 0 is either defined as 1, or it is left undefined.
With some exceptions regarding erroneous values, infinities, and denormalized numbers, Excel calculates in double-precision floating-point format from the IEEE 754 specification [1] (besides numbers, Excel uses a few other data types [2] ). Although Excel allows display of up to 30 decimal places, its precision for any specific number is no ...
For real non-zero values of x, the exponential integral Ei ( x) is defined as. The Risch algorithm shows that Ei is not an elementary function. The definition above can be used for positive values of x, but the integral has to be understood in terms of the Cauchy principal value due to the singularity of the integrand at zero. For complex ...
Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
where a 1 = 0.0705230784, a 2 = 0.0422820123, a 3 = 0.0092705272, a 4 = 0.0001520143, a 5 = 0.0002765672, a 6 = 0.0000430638 erf x ≈ 1 − ( a 1 t + a 2 t 2 + ⋯ + a 5 t 5 ) e − x 2 , t = 1 1 + p x {\displaystyle \operatorname {erf} x\approx 1-\left(a_{1}t+a_{2}t^{2}+\cdots +a_{5}t^{5}\right)e^{-x^{2}},\quad t={\frac {1}{1+px ...
Matrix exponential. In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group .
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3] Rounding errors are due to inexactness in the representation of real numbers and the ...
NaN. In computing, NaN ( / næn / ), standing for Not a Number, is a particular value of a numeric data type (often a floating-point number) which is undefined as a number, such as the result of 0/0. Systematic use of NaNs was introduced by the IEEE 754 floating-point standard in 1985, along with the representation of other non-finite ...