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pro vyhledávání: '"Orr, Derek"'
In this paper, we give elementary proofs of Zagier's formula for multiple zeta values involving Hoffman element and its odd variant due to Murakami. Zagier's formula was a key ingredient in the proof of Hoffman's conjecture. Moreover, using the same
Externí odkaz:
http://arxiv.org/abs/2201.09262
Autor:
Orr, Derek, Ermentrout, Bard
Publikováno v:
Phys. Rev. E 99, 052218 (2019)
In this paper, we study pairs of oscillators that are indirectly coupled via active (excitable) cells. We introduce a scalar phase model for coupled oscillators and excitable cells. We first show that one excitable and one oscillatory cell will exhib
Externí odkaz:
http://arxiv.org/abs/1901.02854
Autor:
Orr, Derek
In this paper, we discuss a similar functional to that of a standard integral. The main difference is in its definition: instead of taking a sum, we are taking a product. It turns out this new "star-integral" may be written in terms of the standard i
Externí odkaz:
http://arxiv.org/abs/1805.01861
Autor:
Orr, Derek
Publikováno v:
J. Comp. Appl. Math. 347 (2019) 330-342
In this paper, we investigate the integral of $x^n\log^m(\sin(x))$ for natural numbers $m$ and $n$. In doing so, we recover some well-known results and remark on some relations to the log-sine integral $\operatorname{Ls}_{n+m+1}^{(n)}(\theta)$. Later
Externí odkaz:
http://arxiv.org/abs/1705.04723
Autor:
Orr, Derek
Publikováno v:
Int. Trans. Spec. Funct. 28:12 (2017) 966-987
In this paper, we find rational zeta series with $\zeta(2n)$ in terms of $\zeta(2k+1)$ and $\beta(2k)$, the Dirichlet beta function. We then develop a certain family of generalized rational zeta series using the generalized Clausen function and use t
Externí odkaz:
http://arxiv.org/abs/1606.04850
Autor:
Lupu, Cezar, Orr, Derek
In this note, using an idea from \cite{Amo-Carrillo-Sanchez} we derive some new series representations involving $\zeta(2n)$ and Euler numbers. Using a well-known series representation for the Clausen function, we also provide some new representation
Externí odkaz:
http://arxiv.org/abs/1605.09541
Autor:
Orr, Derek
Publikováno v:
In Journal of Computational and Applied Mathematics February 2019 347:330-342
Akademický článek
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Akademický článek
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Autor:
Lupu, Cezar, Orr, Derek
Publikováno v:
Ramanujan Journal; Apr2019, Vol. 48 Issue 3, p477-494, 18p