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In mathematics, the factorial of a non-negative integer, denoted by ! , is the product of all positive ... Multiply together the results of the two previous steps;
The product is obtained by multiplying together all factors obtained by substituting the multiplication index for an integer between the lower and the upper values (the bounds included) in the expression that follows the product operator. More generally, the notation is defined as
The term odd factorial is sometimes used for the double factorial of an odd number. [5] [6] The term semifactorial is also used by Knuth as a synonym of double ...
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. [2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9.
These symbols are collectively called factorial powers. [2] The Pochhammer symbol, introduced by Leo August Pochhammer, is the notation (), where n is a non-negative integer. It may represent either the rising or the falling
(To multiply more than 2 expressions, just multiply 2 at a time) To multiply two factors, each term of the first factor must be multiplied by each term of the other factor. If both factors are binomials, the FOIL rule can be used, which stands for "First Outer Inner Last," referring to the terms that are multiplied together. For example, expanding
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 ...