Asymptotic expansions for Riesz fractional derivatives of Airy functions and applications
نویسندگان
چکیده
منابع مشابه
Asymptotic expansions for Riesz fractional derivatives of Airy functions and applications
Riesz fractional derivatives of a function, Dα xf(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, Gi(x). Reduction formulas are provided that allow one to express Riesz potentials of products of Airy fun...
متن کاملAsymptotic Expansions of Fractional Derivatives and Their Applications
We compare the Riemann–Liouville fractional integral (fI) of a function f(z) with the Liouville fI of the same function and show that there are cases in which the asymptotic expansion of the former is obtained from those of the latter and the difference of the two fIs. When this happens, this fact occurs also for the fractional derivative (fD). This method is applied to the derivation of the as...
متن کاملSymbolic Evaluation of Coefficients in Airy-type Asymptotic Expansions
Computer algebra algorithms are developed for evaluating the coefficients in Airy-type asymptotic expansions that are obtained from integrals with a large parameter. The coefficients are defined from recursive schemes obtained from integration by parts. An application is given for the Weber parabolic cylinder function. 1991 Mathematics Subject Classification: 41A60, 33C10, 33C15, 33F05, 65D20.
متن کاملAsymptotic Expansions Methodsand Applications
Feynman diagrams are the most important theoretical tool for particle physicists. They are an efficient link between theory and experiment. However, their translation into actual numerical predictions is often very tedious if not impossible. Huge efforts have been devoted to their evaluation, and several powerful methods have been developed to systemize their treatment. The more complex a Feynm...
متن کاملSuperconvergence Points for the Spectral Interpolation of Riesz Fractional Derivatives∗
In this paper, superconvergence points are located for the approximation of the Riesz derivative of order α using classical Lobatto-type polynomials when α ∈ (0, 1) and generalized Jacobi functions (GJF) for arbitrary α > 0, respectively. For the former, superconvergence points are zeros of the Riesz fractional derivative of the leading term in the truncated Legendre-Lobatto expansion. It is ob...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2009
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.05.029