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On stratifications of Mittag-Leffler's transcendents

Published online by Cambridge University Press:  18 May 2009

Aurel Wintner
Aurel Wintner
Affiliation:
The Johns Hopkins UniversityBaltimore 18, Maryland, U.S.A.
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Guided by an observation of Hausdorff ([4]; reproduced by Whittaker and Robinson [6, pp. 177–178]), I pointed out a long time ago [7] that his “Fourier“ treatment of certain products can be systematized so as to apply to an inclusive class of infinite convolutions. Recently I noticed [8] that an appropriate application of this method supplies the following curious result on gamma-quotients:

Corresponding to every index θ on the range 0 < θ < 1, there exists on the line - ∞ < t < ∞ a monotone function μ = μθ = μθ(t) in terms of which the identity

holds on the half-plane Re z > -1 and so, in particular, on the half-line z ≧0.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 4 , July 1958 , pp. 170 - 172
Copyright
Copyright © Glasgow Mathematical Journal Trust 1958

References

REFERENCES

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