formal series
(0.002 seconds)
21—23 of 23 matching pages
21: 2.6 Distributional Methods
…
►Inserting (2.6.2) into (2.6.1) and integrating formally term-by-term, we obtain
…
►The fact that expansion (2.6.6) misses all the terms in the second series in (2.6.7) raises the question: what went wrong with our process of reaching (2.6.6)? In the following subsections, we use some elementary facts of distribution theory (§1.16) to study the proper use of divergent integrals.
…
22: Bibliography K
…
►
Series expansions for the third incomplete elliptic integral via partial fraction decompositions.
J. Comput. Appl. Math. 207 (2), pp. 331–337.
…
►
Asymptotic expansions of certain -series and a formula of Ramanujan for specific values of the Riemann zeta function.
Acta Arith. 107 (3), pp. 269–298.
…
►
Electromagnetic Fields and Relativistic Particles.
International Series in Pure and Applied Physics, McGraw-Hill Book Co., New York.
…
►
HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
…
►
Quantum-Theoretical Formalism for Inhomogeneous Graded-Index Waveguides.
Akademie Verlag, Berlin-New York.
…
23: 18.38 Mathematical Applications
…
►In consequence, expansions of functions that are infinitely differentiable on in series of Chebyshev polynomials usually converge extremely rapidly.
…
►Linear ordinary differential equations can be solved directly in series of Chebyshev polynomials (or other OP’s) by a method originated by Clenshaw (1957).
…
►However, by using Hirota’s technique of bilinear formalism of soliton theory, Nakamura (1996) shows that a wide class of exact solutions of the Toda equation can be expressed in terms of various special functions, and in particular classical OP’s.
…