On the optimality of a characterization theorem for the gamma function using the multiplication formula |
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Authors: | Hans-Heinrich Kairies |
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Institution: | (1) Institut für Mathematik, Technische Universität Clausthal, Erzstraße 1, D-38678 Clausthal-Zellerfeld, Germany |
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Abstract: | Summary The following Artin type characterization of : + + is proved: Assume thatf: + + satisfies the Gauss multiplication formula for some fixedp 2,f is absolutely continuous on l/p, 1 + ] for some > 0 and lim
x 0
xf(x) = 1. Thenf(x) = (x) forx > 0.The optimality of this result is checked by means of counterexamples. For instance, it is shown that the result is no longer true, if f is absolutely continuous is replaced by f is continuous and of finite variation. |
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Keywords: | Primary 39B22 33B15 Secondary 39B62 |
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