![]() Reprinted, Cambridge University Press, New York, 1962vii+608 MR0178117 0105. ![]() An introduction to the general theory of infinite processes and of analytic functions: with an account of the principal transcendental functions, Fourth edition. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1966 0174.36202 Google Scholar Watanabe, Zum Riemannschen binomischen Lehrsatz, Proc. Marcel Riesz, L'intégrale de Riemann-Liouville et le problème de Cauchy, Acta Math., 81 ( 1949), 1–223 MR0030102 0033.27601 Crossref ISI Google Scholar Weber, Versuch einer allgemeinen Auffasung der Integration und Differentiation The Collected Works of Bernhard Riemann, Dover, New York, 1953, 353–366 Google Scholar Anal., 1 ( 1970), 288–293 10.1137/0501026 MR0260943 0201.44201 Link Google Scholar In probability theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is. Osler, The fractional derivative of a composite function, SIAM J. Osler, Leibniz rule for fractional derivatives generalized and an application to infinite series, SIAM J. Osler, Masters Thesis, Leibniz rule, the chain rule and Taylor's theorem for fractional derivatives, Doctoral thesis, New York University, New York, 1970 Google Scholar Higgins, The use of fractional integral operators for solving nonhomogeneous differential equations, Document, D1-82-0677, Boeing Scientific Research Laboratories, Seattle, Washington, 1967 Google Scholar Higgins, The Rodrigues operator transform, table of generalized Rodrigues formulas, Document, D1-82-04931l, Boeing Scientific Research Laboratories, Seattle, Washington, 1965 Google Scholar Hardy, Riemann's form of Taylor's series, J. , '27 -32 : ( THIRD SERIES :) The London and. Erdélyi, Axially symmetric potentials and fractional integration, J. Do you mean something like this, where you get terms up to some specified total degree fx, y : Sinxy2 + x4y. 43-58, 1814-20 : ( SECOND SERIES :) The Philosophical Magazine, ed. Erdélyi, An integral equation involving Legendre functions, J. in the function you wrote, a,b, but no for c,d) 4 jackmell. (In my expression, is like if only were able to recognize the first 2 as variables of f, i.e. II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954xvi+451 MR0065685 0058.34103 Google Scholar So, let´s focus, the question is if Mathematica is able to do Taylor series expansion of f for all of the 4 variables. H.Tahsiri OffGeneral::spell OffGeneral::spell1. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954xx+391 MR0061695 0055.36401 Google Scholar Please Click on ANIMATION to see the Mathematica code for the above Taylor Series animation. III, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955xvii+292 MR0066496 0064.06302 Google Scholar The Taylor (or more general) series of a function about a point up to order may be found using Series f, x, a, n. Tricomi, Higher transcendental functions. Arthur Erdélyi , , Wilhelm Magnus , , Fritz Oberhettinger and , Francesco G. Here's an example: Here's an example: Going over the syntax: the first argument is the function you want to expand. II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xvii+396 MR0058756 0052.29502 Google Scholar The Mathematica function Series will compute a Taylor series expansion to whatever order you want. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xxvi+302 MR0058756 0051.30303 Google Scholar One can either use SumConvergence or Sum with GenerateConditions -> True (thanks to a comment by Artes).Arthur Erdélyi , , Wilhelm Magnus , , Fritz Oberhettinger and , Francesco G.
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