Abstract
We have defined (Set Theory, III, p. 179) the function n! for every integer n ≥ 0, as equal to the product \(\prod\limits_{0 \leqslant k \leqslant n} {(n - k)}\); so 0!=1 and (n+1)!=(n+1)n! for n ≥ 0. We set г(n) = (n − 1)! for each integer n ≥ 1; we propose to define, on the set of real numbers x > 0, a continuous function г(x) extending the function г defined on the set of integers ≥ 1.
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© 2004 Springer-Verlag Berlin Heidelberg
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Theory, E., Spain, P. (2004). The Gamma function. In: Elements of Mathematics Functions of a Real Variable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59315-4_8
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DOI: https://doi.org/10.1007/978-3-642-59315-4_8
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