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pro vyhledávání: '"Coffey, Mark W."'
Autor:
Coffey, Mark W.
Let $\eta$ be the weight $1/2$ Dedekind function. A unification and generalization of the integrals $\int_0^\infty f(x)\eta^n(ix)dx$, $n=1,3$, of Glasser \cite{glasser2009} is presented. Simple integral inequalities as well as some $n=2$, $4$, $6$, $
Externí odkaz:
http://arxiv.org/abs/1901.07168
Autor:
Coffey, Mark W.
First some definite integrals of W. H. L. Russell, almost all with trigonometric function integrands, are derived, and many generalized. Then a list is given in Russell-style of generalizations of integral identities of Amdeberhan and Moll. We conclu
Externí odkaz:
http://arxiv.org/abs/1806.07962
Autor:
Coffey, Mark W.
The well known table of Gradshteyn and Ryzhik contains indefinite and definite integrals of both elementary and special functions. We give proofs of several entries containing integrands with some combination of hyperbolic and trigonometric functions
Externí odkaz:
http://arxiv.org/abs/1803.00632
The (generalised) Mellin transforms of certain Chebyshev and Gegenbauer functions based upon the Chebyshev and Gegenbauer polynomials, have polynomial factors $p_n(s)$, whose zeros lie all on the `critical line' $\Re\,s=1/2$ or on the real axis (call
Externí odkaz:
http://arxiv.org/abs/1703.09251
Autor:
Coffey, Mark W.
The Stieltjes constants $\gamma_k(a)$ appear in the regular part of the Laurent expansion for the Hurwitz zeta function $\zeta(s,a)$. We present summatory results for these constants $\gamma_k(a)$ in terms of fundamental mathematical constants such a
Externí odkaz:
http://arxiv.org/abs/1701.07064
Autor:
Coffey, Mark W.
We illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class problem Hamil
Externí odkaz:
http://arxiv.org/abs/1701.05584
Autor:
Coffey, Mark W.
The Riemann zeta identity at even integers of Lettington, along with his other Bernoulli and zeta relations, are generalized. Other corresponding recurrences and determinant relations are illustrated. Another consequence is the application to sums of
Externí odkaz:
http://arxiv.org/abs/1601.01673
Autor:
Coffey, Mark W.
The Stieltjes constants $\gamma_k(a)$ appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function $\zeta(s,a)$ about $s=1$. We generalize the integral and Stirling number series results of [4] for $\gamma_k(a=
Externí odkaz:
http://arxiv.org/abs/1602.03387
Autor:
Coffey, Mark W.
We principally present reductions of certain generalized hypergeometric functions $_3F_2(\pm 1)$ in terms of products of elementary functions. Most of these results have been known for some time, but one of the methods, wherein we simultaneously solv
Externí odkaz:
http://arxiv.org/abs/1506.09160
We study higher-dimensional interlacing Fibonacci sequences, generated via both Chebyshev type functions and $m$-dimensional recurrence relations. For each integer $m$, there exist both rational and integer versions of these sequences, where the unde
Externí odkaz:
http://arxiv.org/abs/1502.03085