factorial power造句

• }} denotes the rising factorial power in the notation of D . E . Knuth.
• In other words, the " n "-th factorial moment measure is the expectation of the " n " th factorial power of some point process.
• This definition can be contrasted with the definition of the " n "-factorial power of a point process for which each " n "-tuples consists of " n " points.
• Therefore instead of by an ordinary power of " x ", the value is given by a falling factorial power of " x ", in which each successive factor is one fewer than the previous one.
• For some positive integer \ textstyle n = 1, 2, \ ldots, the \ textstyle n-th factorial power of a point process \ textstyle { N } on \ textstyle \ textbf { R } ^ d is defined as:
• The product is well defined without the assumption that n is a non-negative integer and is of importance outside combinatorics as well; it is known as the Pochhammer symbol ( n ) _ k or as the k-th falling factorial power n ^ { \ underline k } of n.
• The summation in the above expression is performed over all \ textstyle n-tuples of distinct points, including permutations, which can be contrasted with the definition of the multiplication while the existence of various point process notation means that the " n "-th factorial power of a point process is sometimes defined using other notation.