“Double Factorial”的概念、定义、习题解题方法及翻译-数学辞典

单词

Double Factorial

释义

Double Factorial

The double factorial is a generalization of the usual Factorial defined by

(1)

For

, 1, 2, ..., the first few values are 1, 1, 2, 3, 8, 15, 48, 105, 384, ... (Sloane's A006882).

There are many identities relating double factorials to Factorials. Since





	(2)

it follows that

. Since


			(3)

it follows that

. Since





	(4)

it follows that

(5)

Similarly, for

, 1, ...,

(6)

For

Odd,


			(7)

For

Even,


			(8)

Therefore, for any

(9)

(10)

The double factorial is a special case of the Multifactorial.

See also Factorial, Multifactorial

References

Sloane, N. J. A. SequenceA006882/M0876in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

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