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By applying the MC algorithm and the Bauer-Muir transformation for continued fractions, in this paper we shall give six examples to show how to establish an infinite set of continued fraction formulas for certain Ramanujan-type series, such as Catalans constant, the exponential function, etc.
We give an estimate of the general divided differences $[x_0,dots,x_m;f]$, where some of the $x_i$s are allowed to coalesce (in which case, $f$ is assumed to be sufficiently smooth). This estimate is then applied to significantly strengthen Whitney a
We establish partial semigroup property of Riemann-Liouville and Caputo fractional differential operators. Using this result we prove theorems on reduction of multi-term fractional differential systems to single-term and multi-order systems, and prov
Using the Laplace derivative a Perron type integral, the Laplace integral, is defined. Moreover, it is shown that this integral includes Perron integral and to show that the inclusion is proper, an example of a function is constructed, which is Lapla
In this paper we show a deterministic parallel all-pairs shortest paths algorithm for real-weighted directed graphs. The algorithm has $tilde{O}(nm+(n/d)^3)$ work and $tilde{O}(d)$ depth for any depth parameter $din [1,n]$. To the best of our knowled
A New Trinomial Recombination Tree Algorithm and Its Applications