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The factorial of is , or in symbols, ! =. There are several motivations for this definition: For n = 0 {\displaystyle n=0} , the definition of n ! {\displaystyle n!} as a product involves the product of no numbers at all, and so is an example of the broader convention that the empty product , a product of no factors, is equal to the ...
From this it follows that the rightmost digit is always 0, the second can be 0 or 1, the third 0, 1 or 2, and so on (sequence A124252 in the OEIS).The factorial number system is sometimes defined with the 0! place omitted because it is always zero (sequence A007623 in the OEIS).
The value of each is taken to be 1 (an empty product) when =. 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.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
The factorial 0! evaluates to 1, as a special case of the empty product. ... using an "alphabet" that contains only two symbols, usually chosen to be "0" and "1".
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
Following the usual convention for the empty product, the hyperfactorial of 0 is 1. The sequence of hyperfactorials, beginning with H ( 0 ) = 1 {\displaystyle H(0)=1} , is: [ 1 ] 1, 1, 4, 108, 27648, 86400000, 4031078400000, 3319766398771200000, ...
The zero double factorial 0‼ = 1 as an empty product. [3] [4] ... in terms of the Pochhammer symbol and the generalized, rational-valued binomial coefficients as ...