RealDigits can be used to return a list of digits of E and ContinuedFraction to obtain terms of its continued fraction expansion. In fact, calculating the first million decimal digits of E takes only a fraction of a second on a modern desktop computer. E can be evaluated to arbitrary numerical precision using N.Despite its extensive appearance in various closed-form sums and integrals, E is conjectured to not be a Kontsevich –Zagier period (meaning it is not the value of an absolutely convergent integral of any univariate or multivariate rational function with rational coefficients over algebraically-specified domains in ). lt is not known if E is normal (meaning the digits in its base- b expansion are equally distributed) to any base. However, E is the "least" transcendental number possible since it has irrationality measure of 2. Euler proved that E is irrational (meaning it cannot be expressed as a ratio of any two integers) and Hermite subsequently established that it is transcendental (meaning it is not the root of any integer polynomial).Expansion and simplification of complicated expressions involving E may require use of functions such as FunctionExpand and FullSimplify. When E is used as a symbol, it is propagated as an exact quantity. The exponential function Exp is converted to E^ x.It appears in many sums, products, integrals, in equations involving the compounding of interest, in growth laws involving exponential growth or decay, and in formulas from a wide range of other mathematical and scientific fields. With the possible exception of Pi, E is the most important constant in mathematics. E has a number of equivalent definitions in mathematics, including as the infinite sum of reciprocal factorials over non-negative integers and as the limiting value. It is also known as Euler's number and can be input as \. ExponentialGeneratingFunctionexpr, n, x gives the exponential generating function in x for the sequence whose nNullth term is given by the expression. ![]()
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