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exp is a fixed point of derivative as a linear operator on function space. If a variable's growth or decay rate is proportional to its size—as is the case in unlimited population growth (see Malthusian catastrophe ), continuously compounded interest , or radioactive decay —then the variable can be written as a constant times an exponential ...
In computer programming, an S-expression (or symbolic expression, abbreviated as sexpr or sexp) is an expression in a like-named notation for nested list (tree-structured) data. S-expressions were invented for and popularized by the programming language Lisp, which uses them for source code as well as data.
The last expression is the logarithmic mean. = ( >) = (>) (the Gaussian integral) = (>) = (, >) (+) = (>)(+ +) = (>)= (>) (see Integral of a Gaussian function
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a ...
The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .
The six most common definitions of the exponential function = for real values are as follows.. Product limit. Define by the limit: = (+).; Power series. Define e x as the value of the infinite series = =! = + +! +! +! + (Here n! denotes the factorial of n.
Recall from above that an n×n matrix exp(tA) amounts to a linear combination of the first n −1 powers of A by the Cayley–Hamilton theorem. For diagonalizable matrices, as illustrated above, e.g. in the 2×2 case, Sylvester's formula yields exp(tA) = B α exp(tα) + B β exp(tβ), where the B s are the Frobenius covariants of A.