The Gamma function

Elementary Theory and Philip Spain ()
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Philip Spain: University of Glasgow, Department of Mathematics

Chapter Chapter VII in Elements of Mathematics Functions of a Real Variable, 2004, pp 305-331 from Springer

Abstract: 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.

Date: 2004
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DOI: 10.1007/978-3-642-59315-4_8

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