Search results
Results from the WOW.Com Content Network
The exponential factorials grow much more quickly than regular factorials or even hyperfactorials. The number of digits in the exponential factorial of 6 is approximately 5 × 10 183 230 . The sum of the reciprocals of the exponential factorials from 1 onwards is the following transcendental number :
In mathematical analysis, factorials are used in power series for the exponential function and other functions, and they also have applications in algebra, number theory, probability theory, and computer science. Much of the mathematics of the factorial function was developed beginning in the late 18th and early 19th centuries.
This last non-simple continued fraction (sequence A110185 in the OEIS), equivalent to = [;,,,,,...], has a quicker convergence rate compared to Euler's continued fraction formula [clarification needed] and is a special case of a general formula for the exponential function:
2.2 Exponential function 2.3 Trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions relationship 2.4 Modified-factorial denominators
The exponential function is the sum of the power series [2] [3] = + +! +! + = =!, where ! is the factorial of n (the product of the n first positive integers). This series is absolutely convergent for every x {\displaystyle x} per the ratio test .
The partial sum formed by the first n + 1 terms of a Taylor series is ... n! denotes the factorial of n. The function f ... numbers is the exponential function of the ...
Exponential dispersion model; Exponential distribution; Exponential error; Exponential factorial; Exponential family; Exponential field; Exponential formula; Exponential function; Exponential generating function; Exponential-Golomb coding; Exponential growth; Exponential hierarchy; Exponential integral; Exponential integrator; Exponential map ...
The definition of e x as the exponential function allows defining b x for every positive real numbers b, in terms of exponential and logarithm function. Specifically, the fact that the natural logarithm ln(x) is the inverse of the exponential function e x means that one has = () = for every b > 0.