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multiplication formula for gamma function
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(Theorem)
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For any integer $n > 0$ , the gamma function satisfes the following relation:
$$\Gamma (nz) = (2 \pi)^{n - 1 \over 2} n^{nz - {1 \over 2}} \prod\limits_{k=0}^{n-1} \Gamma \left( z + {k \over n} \right)$$
This equation is true for all complex values of $z$ for which both sides are defined.
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"multiplication formula for gamma function" is owned by rspuzio.
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Cross-references: sides, complex, equation, relation, gamma function, integer
This is version 5 of multiplication formula for gamma function, born on 2004-10-13, modified 2004-10-14.
Object id is 6368, canonical name is MultiplicationFormulaForGammaFunction.
Accessed 2947 times total.
Classification:
| AMS MSC: | 33B15 (Special functions :: Elementary classical functions :: Gamma, beta and polygamma functions) | | | 30D30 (Functions of a complex variable :: Entire and meromorphic functions, and related topics :: Meromorphic functions, general theory) |
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Pending Errata and Addenda
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