Exponential and Logarithmic Functions

Exponential Function shifted, eToThePower(X) − 1: ExpL(x) = x + x^2 / 2! + x^3 / 3! ...
Evaluates to one less than e raised to the x power, where e is the base of the
natural logarithms. This function is needed when an expression contains Exp(x) − 1
and x can take on small values. ExpL(x) is accurate for small x.

Exponential Function: Exp(x) = ExpL(x) + 1
See: Exponential Function -- From MathWorld
and Wolfram Function Evaluation

Power Functions, x^y: Pow(x, y) = +/−Exp(y * Ln(|x|)),
If x > 0, x^y = Exp(y * Ln(x)),
Else if x = 0 and y = 0, 0^0 = 1,
Else if x = 0 and y > 0, 0^pos = 0,
Else if x = 0 and y < 0, 0^neg = error,
Else if x < 0 and y is not an integer, error,
Else if x < 0 and y is an even integer, x^y = Exp(y * Ln(|x|)),
Else if x < 0 and y is an odd integer, x^y = −Exp(y * Ln(|x|)).
See: Power -- From MathWorld
and Wolfram Function Evaluation

Square: Sq(x) = x^2 = x*x.
See: Square -- From MathWorld
and Wolfram Function Evaluation

Square Root, The positive Square Root function: SqRt(x) = x^(1/2) = Pow(x, 1/2),
Of the two roots, the one with its value >= 0 is taken,
if x < 0, error.
See: Square Root -- From MathWorld
and Wolfram Function Evaluation

Cube Root, CuRt(x) = x^(1/3) = +/−Pow(|x|, 1/3),
If x = 0, CuRt(0) = 0,
Else if x > 0, CuRt(x) = Pow(x, 1/3),
Else if x < 0, CuRt(x) = −Pow(|x|, 1/3).
See: Cube Root -- From MathWorld
and Wolfram Function Evaluation

Natural Logarithm shifted, Log base e of 1+x: LnL(x) = Ln(1+x) = Ln((1+z)/(1−z)) = 2 * (z + z^3/3 + z^5/5 ...),
where z = x / (2+x), but not defined for x <= −1.
This function is needed when an expression contains Ln(1+x) and x can take on a value near zero.
LnL(x) is accurate for values of x near zero.

Natural Logarithm, Log base e of x: Ln(x) = LnL(x−1),
but not defined for x <= 0.
See: Natural Logarithm -- From MathWorld
and Wolfram Function Evaluation

Logarithm, Log base b of x: LogB(b, x) = Ln(x)/Ln(b),
but not defined for x <= 0 or b <= 0.
See: Logarithm -- From MathWorld
and Wolfram Function Evaluation

Common Logarithm, Log base 10 of x: Log(x) = LogB(10, x) = Ln(x)/Ln(10),
but not defined for x <= 0.
See: Common Logarithm -- From MathWorld
and Wolfram Function Evaluation

See: Transcendental Function Evaluation

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This page accessed times since Feb 16, 2006.
Page created by: hjsmithh@sbcglobal.net
Changes last made on Monday, 06-Aug-07 20:47:17 PDT