Search results
Results from the WOW.Com Content Network
In mathematics, the factorial of a non-negative integer, denoted by !, is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: ! = () = ()! For example, ! =! = =
For =, the sum of the factorials of the digits is simply the number of digits in the base 2 representation since ! =! =. A natural number n {\displaystyle n} is a sociable factorion if it is a periodic point for SFD b {\displaystyle \operatorname {SFD} _{b}} , where SFD b k ( n ) = n {\displaystyle \operatorname {SFD} _{b}^{k}(n)=n} for a ...
2.4 Modified-factorial denominators. 2.5 Binomial coefficients. 2.6 Harmonic numbers. 3 Binomial coefficients. 4 Trigonometric functions. 5 Rational functions.
[1] [2] [3] One way of stating the approximation involves the logarithm of the factorial: (!) = + (), where the big O notation means that, for all sufficiently large values of , the difference between (!
Clearly the next factorial number representation after 5:4:3:2:1:0! is 1:0:0:0:0:0:0! which designates 6! = 720 10, the place value for the radix-7 digit. So the former number, and its summed out expression above, is equal to:
The sum of the reciprocals of the square numbers (the Basel problem) is the transcendental number π 2 / 6 , or ζ(2) where ζ is the Riemann zeta function. The sum of the reciprocals of the cubes of positive integers is called Apéry's constant ζ(3) , and equals approximately 1.2021 .
Unrooted binary trees with n + 5 / 2 labeled leaves. Each such tree may be formed from a tree with one fewer leaf, by subdividing one of the n tree edges and making the new vertex be the parent of a new leaf. Rooted binary trees with n + 3 / 2 labeled leaves. This case is similar to the unrooted case, but the number of edges ...
In this article, the symbol () is used to represent the falling factorial, and the symbol () is used for the rising factorial. These conventions are used in combinatorics , [ 4 ] although Knuth 's underline and overline notations x n _ {\displaystyle x^{\underline {n}}} and x n ¯ {\displaystyle x^{\overline {n}}} are increasingly popular.