Dois teoremas sôbre a função gama
DOI:
https://doi.org/10.1590/S0071-12761956000100006Abstract
This paper proves the following theorems on the gamma function: Theorem I The integral ∫O∞ t u e-t dt = Γ ( u + 1 ) , where u, real or complex, is such that R (u) > -1, will not change its value if we substitute z = Q (cos φ + i sen φ) for the real variable t, being jconstant and such that - Π/2 < φ < Π/2 , Theorem II The integral ∫-∞∞ w2u + 1 e -w² dw = Γ ( u + 1 ) , where 2u + 1 is supposed to be a non negative even integer, will not change its value if we substitute z = w + fi, f being a real constant, for the real variable w. The proof of both theorems is obtained by means of the well known Cauchy theorem on contour integrals on the complex plane, as suggested by CRAMÉR (1, p. 126) and LEVY (3, p. 178).Downloads
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Published
1956-01-01
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How to Cite
Gomes, F. P. (1956). Dois teoremas sôbre a função gama. Anais Da Escola Superior De Agricultura Luiz De Queiroz, 12, 149-158. https://doi.org/10.1590/S0071-12761956000100006