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Fractional Powers of Hyperfunctions h, s and \( \frac{I}{{S - \alpha }} \)

  • K. Yosida
Chapter
  • 338 Downloads
Part of the Applied Mathematical Sciences book series (AMS, volume 55)

Abstract

These functions are respectively defined by Euler’s* integrals:
$$\Gamma \left( \lambda \right) = \int_{0}^{\infty } {{{t}^{{\lambda - 1}}}{{e}^{{ - t}}}dt(Re\lambda > 0)**,}$$
(1)
$$ B(\lambda ,\mu ) = {\text{ }}\int_0^1 {{t^{\lambda - 1}}{{(1 - t)}^{\mu - 1}}dt (Re \lambda > 0, Re \mu > 0).} $$
(12.2)

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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • K. Yosida
    • 1
  1. 1.Kamakura 247Japan

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