Remainder Term Estimates of the Renewal Function
نویسندگان
چکیده
منابع مشابه
On the Quantitative Estimates of the Remainder in Normal Forms
We consider an analytic Hamiltonian system with three degrees of freedom and having a family of periodic orbits with a transition stability complex instability We reduce the Hamiltonian to a normal form around a transition periodic orbit and we obtain H Z r R r The analysis of the truncated normal form Z r allows the description of a Hopf bifurcation of D tori However this communication will co...
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In the present paper we obtain enhanced estimates regarding the remainder of the alternating harmonic series. More precisely, we show that 1 4n2 +a < ∣ ∣∣ ∣ ∣ n ∑ k=1 (−1)k−1 1 k − (−1)n−1 1 2n − ln2 ∣ ∣∣ ∣ ∣ 1 4n2 +b , for all n ∈N , with a = 2 and b = 2(3−4 ln2) 2 ln2−1 = 1.177398899 . . . . In addition, the constants a and b are the best possible with the above-mentioned property. Mathematic...
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15 صفحه اولThe remainder term for analytic functions of symmetric Gaussian quadratures
For analytic functions the remainder term of Gaussian quadrature rules can be expressed as a contour integral with kernel Kn. In this paper the kernel is studied on elliptic contours for a great variety of symmetric weight functions including especially Gegenbauer weight functions. First a new series representation of the kernel is developed and analyzed. Then the location of the maximum modulu...
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Remainder estimates for Levin-type sequence transformations are discussed. A new remainder estimate is introduced which is related to the Kummer transformation. Test cases are presented which show that the new remainder estimate can enhance the performance of Levin-type sequence transformations considerably.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1983
ISSN: 0091-1798
DOI: 10.1214/aop/1176993664