منابع مشابه
Dual series equations involving generalized Laguerre polynomials
where α + β + 1 > β > 1 −m, σ + 1 > α + β > 0, m is a positive integer, and 0 < h < ∞, 0 ≤ b <∞, and h and b are finite constants. L n [(x + b)h] is a Laguerre polynomial, An are unknown coefficients, and f (x) and g(x) are prescribed functions. Srivastava [5, 6] has solved the following dual series equations: ∞ ∑ n=0 AnL (α) n (x) Γ(α+n+ 1) = f (x), 0 < x < a, (1.3) ∞ ∑ n=0 AnL (σ) n (x) Γ(α+n...
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The main purpose of this paper is to describe and analyse techniques for the numerical solution of highily oscillatory ordinary differential equations by exploying a Neumann expansion. Once the variables in the differential system are changed with respect to a rapidly rotating frame of reference, the Neumann method becomes very effective indeed. However, this effectiveness rests upon suitable q...
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This section collects the standard terminology and results used in the sequel (see [5]). Let I = [a,b] be an interval of real numbers. C1(I ,I), the set of all continuously differentiable functions from I into I , is a closed subset of the Banach Space C1(I ,R) of all continuously differentiable functions from I into R with the norm ‖ · ‖c1 defined by ‖φ‖c1 = ‖φ‖c0 +‖φ′‖c0 , φ∈ C1(I ,R) where ‖...
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Let f be a self-mapping on a topological space X and f denote the mth iterate of f , that is, f f ◦ fm−1, f0 id, m 1, 2, . . . . Let C X,X be the set of all continuous self-mappings on X. Equations having iteration as their main operation, that is, including iterates of the unknown mapping, are called iterative equations. It is one of the most interesting classes of functional equations 1–4 , b...
متن کاملSeries involving Arithmetric Functions
We intend here to collect infinite series, each involving unusual combinations or variations of well-known arithmetic functions. For simplicity’s sake, results are often quoted not with full generality but only to illustrate a special case. Let σ(n) denote the sum of all distinct divisors of n, κ(n) denote the quotient of n with its greatest square divisor, and φ(n) denote the number of positiv...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1975
ISSN: 1385-7258
DOI: 10.1016/1385-7258(75)90011-6