Related papers: Creative Telescoping for Holonomic Functions
Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in computer algebra. At the…
Creative telescoping is a powerful computer algebra paradigm -initiated by Doron Zeilberger in the 90's- for dealing with definite integrals and sums with parameters. We address the mixed continuous-discrete case, and focus on the…
The power of robotic telescopes to transform science education has been voiced by multiple sources, since the 1980s. Since then, much technical progress has been made in robotic telescope provision to end users via a variety of different…
The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our complexity-driven approach is to obtain…
For given multivariate functions specified by algebraic, differential or difference equations, the separability problem is to decide whether they satisfy linear differential or difference equations in one variable. In this paper, we will…
Astrophotonics is a burgeoning field that lies at the interface of photonics and modern astronomical instrumentation. Here we provide a pedagogical review of basic photonic functions that enable modern instruments, and give an overview of…
Artificial intelligence technology has been widely used in astronomy, and new artificial intelligence technologies and application scenarios are constantly emerging. There have been a large number of papers reviewing the application of…
Much of the progress in Astronomy has been driven by instrumental developments, from the first telescopes to fiber fed spectrographs. In this review we describe the field of astrophotonics, a combination of photonics and astronomical…
Since its emergence two decades ago, astrophotonics has found broad application in scientific instruments at many institutions worldwide. The case for astrophotonics becomes more compelling as telescopes push for AO-assisted,…
The next major advancement in astronomy and cosmology will be driven by deep observations using very sensitive telescopes with high spatial and spectral resolution capabilities. An international consortium of astronomers, including Indian…
The fields of Astronomy and Astrophysics are technology limited, where the advent and application of new technologies to astronomy usher in a flood of discoveries altering our understanding of the Universe (e.g., recent cases include LIGO…
Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums by synthesizing summands that telescope, called certificates. We describe a creative telescoping algorithm that computes telescopers for definite…
Bold colour images from telescopes act as extraordinary ambassadors for research astronomers because they pique the public's curiosity. But are they snapshots documenting physical reality? Or are we looking at artistic spacescapes created…
The introduction of new tools in people's workflow has always been promotive of new creative paths. This paper discusses the impact of using computational tools in the performance of creative tasks, especially focusing on graphic design.…
Astrophotonics is the application of versatile photonic technologies to channel, manipulate, and disperse guided light from one or more telescopes to achieve scientific objectives in astronomy in an efficient and cost-effective way. The…
The study of integrating photonic devices into astronomical instruments is the primary focus of astrophotonics. The growth in this area of study is relatively recent. Research related to astronomical spectroscopic phenomena has received a…
Creative telescoping applied to a bivariate proper hypergeometric term produces linear recurrence operators with polynomial coefficients, called telescopers. We provide bounds for the degrees of the polynomials appearing in these operators.…
The past fifty years have been an epoch of impressive progress in the field of astronomical technology. Practically all the technical tools, which we use today, have been developed during that time span. While the first half of this period…
The Hubble Space Telescope's mission is summarized, with special emphasis placed on the Space Telescope Science Institute's unique experience with Hubble's behavior as an astronomical telescope in the environment of low earth orbit for over…
Astronomers have come to recognize the benefits of photonics, often in combination with optical systems, in solving longstanding experimental problems in Earth-based astronomy. Here, we explore some of the recent advances made possible by…