Abstract
These functions are respectively defined by Euler’s* integrals:
Leonhard Euler (1707-1783)
tλ−1 = exp ((λ−1)log t) taking the principal value of log t for t > 0 so that |tλ−1| = exp ((Re λ−1)log t). Hence the integrals in (12.1) and in (12.2) are convergent.
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© 1984 Springer Science+Business Media New York
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Yosida, K. (1984). Fractional Powers of Hyperfunctions h, s and \( \frac{I}{{S - \alpha }} \). In: Operational Calculus. Applied Mathematical Sciences, vol 55. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1118-1_4
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DOI: https://doi.org/10.1007/978-1-4612-1118-1_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96047-0
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