منابع مشابه
A note on the fast power series' exponential
It is shown that the exponential of a complex power series up to order n can be implemented via (23/12+o(1))M(n) binary arithmetic operations over C, where M(n) stands for the (smoothed) complexity of multiplication of polynomials of degree < n in FFT-model. Yet, it is shown how to raise a power series to a constant power with the complexity (27/8 + o(1))M(n).
متن کاملA Note on Stirling Series
We study sums S = S(d, n, k) = ∑ j≥1 [ d] jk( j )j! with d ∈ N = {1, 2, . . . } and n, k ∈ N0 = {0, 1, 2, . . . } and relate them to (finite) multiple zeta functions. As a byproduct of our results we obtain asymptotic expansions of ζ(d + 1) −H n as n tends to infinity. Furthermore, we relate sums S to Nielsen’s polylogarithm.
متن کاملOn Interpolating Power Series
We derive a simple error estimate for equally spaced, polynomial interpolation of power series that does not require the uniform bounds on derivatives of the Cauchy remainder. The key steps are expressing Newton coefficients in terms of Stirling numbers S(i, j) of the second kind and applying the concavity of lnS(i, j).
متن کاملA note on lacunary series in $mathcal{Q}_K$ spaces
In this paper, under the condition that $K$ is concave, we characterize lacunary series in $Q_{k}$ spaces. We improve a result due to H. Wulan and K. Zhu.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1947
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1947-08886-8