General Euler-Boole's and dual Euler-Boole's formulae
نویسندگان
چکیده
منابع مشابه
General Euler-Ostrowski formulae and applications to quadratures
The aim of this paper is to generalize inequality 0096-3 doi:10 * Co E-m f ðxÞ 1 b a Z b a f ðs1Þds1 f ðbÞ f ðaÞ b a x aþ b 2 f 0ðbÞ f 0ðaÞ 2ðb aÞ x 2 ðaþ bÞxþ a 2 þ b þ 4ab 6 6 kf k1 ðb aÞ 3 6 I x a b a obtained in [A. Aglić Aljinović, M. Matić, J. Pečarić, Improvements of some Ostrowski type inequalities, J. Comput. Anal. Appl., in press], and therefore obtain a generalization and improvement...
متن کاملAnalogues of Euler and Poisson summation formulae
Abstract. Euler–Maclaurin and Poisson analogues of the summations ∑a<n≤b χ(n) f (n), ∑a<n≤b d(n) f (n), ∑a<n≤b d(n)χ(n) f (n) have been obtained in a unified manner, where (χ(n)) is a periodic complex sequence; d(n) is the divisor function and f (x) is a sufficiently smooth function on [a,b]. We also state a generalised Abel’s summation formula, generalised Euler’s summation formula and Euler’s...
متن کاملUnusual Formulae for the Euler Characteristic
Everyone knows that the Euler characteristic of a combinatorial manifold is given by the alternating sum of its numbers of simplices. It is shown that there are other linear combinations of the numbers of simplices which are combinatorial invariants, but that all such invariants are multiples of the Euler characteristic. Theorem [Pachner 1987, [3]]. Two closed combinatorial n-manifolds are PLho...
متن کاملGeneral Euler Diagram Generation
Euler diagrams are a natural method of representing set-theoretic data and have been employed in diverse areas such as visualizing statistical data, as a basis for diagrammatic logics and for displaying the results of database search queries. For effective use of Euler diagrams in practical computer based applications, the generation of a diagram as a set of curves from an abstract description ...
متن کاملOn Generalized Dual Euler Angles
This paper first explores the generalization of Euler angles to the case in which the rotation axes are not necessarily members of an orthonormal triad, and presents a concise solution to their computation that relies on the calculation of standard Euler angles. Then, this generalization is taken one step further by introducing translations, that is, by defining generalized Euler angles about s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2005
ISSN: 1331-4343
DOI: 10.7153/mia-08-27