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The Riemann ζ function and asymptotics for Stieltjes fractions

✍ Scribed by Joris Van Deun


Publisher
Springer US
Year
2009
Tongue
English
Weight
385 KB
Volume
21
Category
Article
ISSN
1382-4090

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We extend the Stieltjes integral to Hölder functions of two variables and prove an existence and uniqueness result for the corresponding deterministic ordinary differential equations and also for stochastic equations driven by a two-parameter fractional Brownian motion.

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## Riesz fractional derivatives of a function, D α x f (x) (also called Riesz potentials), are defined as fractional powers of the Laplacian. Asymptotic expansions for large x are computed for the Riesz fractional derivatives of the Airy function of the first kind, Ai(x), and the Scorer function, G