3 edition of **Computational techniques for the summation of series** found in the catalog.

Computational techniques for the summation of series

Anthony Sofo

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- 0 Currently reading

Published
**2004** by Kluwer Academic/Plenum Publishers in New York .

Written in English

**Edition Notes**

Statement | Anthony Sofo. |

Classifications | |
---|---|

LC Classifications | QA76 |

The Physical Object | |

Pagination | xv, 189 p. : |

Number of Pages | 189 |

ID Numbers | |

Open Library | OL22597564M |

ISBN 10 | 0306478056 |

SUMMATION OF SERIES USING COMPLEX VARIABLES Another way to sum infinite series involves the use of two special complex functions, namely-where f(z) is any function with a finite number of poles at z 1, z 2,.. z N within the complex plane and cot(B z) and csc(Bz) have the interesting property that they have simple poles at all theFile Size: 77KB. Computational techniques for fluid dynamics Clive A. J. Fletcher The purpose of this textbook is to provide senior undergraduate and postgraduate engineers, scientists and applied mathematicians with the specific techniques, and the framework to develop skills in using the techniques, that have proven effective in the various brances of. Summer, summer, summertime. Time to sit back and unwind. Or get your hands on some free machine learning and data science books and get your learn on. . scientists or engineers who just want to use convergence acceleration and summation techniques as computational tools in order to get their work done. The problems with these mathematically oriented books become particularly obvious in the case of Sidi’s book on sequence transformations [75], which is the most recent monograph on this topic.

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No book of this type exists which attempts to give a link, by developing a comprehensive method, between non-hypergeometric and hypergeometric summation. This book is intended for use in the fields of applied mathematics, analysis, non-hypergeometric and hypergeometric summation, summation of series and automated techniques."Cited by: Computational Techniques for the Summation of Series - Kindle edition by Sofo, Anthony.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Computational Techniques for the Summation of cturer: Springer.

Computational Techniques for the Summation of Series is a text on the representation of series in closed form. The book presents a unified treatment of summation of sums and series using function theoretic methods. A technique is developed based on residue theory that is useful for the summation of Brand: Springer US.

"Computational Techniques for the Summation of Series is a text on the representation of series in closed form. The book presents a unified treatment of the summation of sums and series using function theoretic methods.

Computational Techniques for the Summation of Series is a text on the representation of series in closed form. The book presents a unified treatment of summation of sums and series using function theoretic methods. A technique is developed based on residue theory that is useful for the summation of series of both Hypergeometric and Non.

Request PDF | On Jan 1,Anthony Sofo and others published Computational Techniques for the Summation of Series | Find, read and cite all the research you need on ResearchGateAuthor: Anthony Sofo. "This book collects in one volume the author’s considerable results in the area of the summation of series and their representation in closed form, and details the techniques by which they have been obtained the calculations are given in plenty of detail, and closely related work which has appeared in a variety of places is conveniently collected together.".

This book is intended for use in the fields of applied mathematics, analysis, non-hypergeometric and hypergeometric summation, summation of series and automated techniques." (Antonio Lopez-Carmona, Zentralblatt MATH, Vol.

(10), ). Buy Computational Techniques for the Summation of Series Softcover reprint of the original 1st ed. by Anthony Sofo (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders. Sofo, Anthony () Computational Techniques for the Summation of Series.

Kluwer Academic Publishers, New York. Full text for this resource is not available from the Research Repository. Cite this chapter as: Sofo A. () Hypergeometric Summation: Fibonacci and Related Series. In: Computational Techniques for the Summation of : Anthony Sofo.

“The book under review deals with the modern algorithmic techniques for hypergeometric summation, most of which were introduced in the ’s. This well-written book should be recommended for anybody who is interested in binomial summations and special : Springer-Verlag London. Note: If you're looking for a free download links of Computational Techniques for the Summation of Series Pdf, epub, docx and torrent then this site is not for you.

only do ebook promotions online and we does not distribute any free download of ebook on this site. In the great book Computational Techniques for the Summation of Series [6], Anthony Sofo provides the following series, which results from integrating the series repeatedly: () Multiply () by x, replace x with sinx and integrate, then, of course, substitute ().

Thus, Theorem 10 holds. Other Series The following series is given in [5]. Computational Techniques for the Summation of Series. [Anthony Sofo] -- <STRONG>Computational Techniques for the Summation of Series</STRONG> is a text on the representation of series in closed form.

Read "Computational Techniques for the Summation of Series" by Anthony Sofo available from Rakuten Kobo. "This book collects in one volume the author’s considerable results in the area of the summation of series and their rep Brand: Springer US.

I consider this a historic book, really, and I bought it to compare summation techniques of over half a century ago with those available today (quite a progress). This book should be no longer used for teaching, self-teaching, or boning up.

But it provides some good insights into the history of mathematics/5(5). SERIES: A series is simply the sum of the various terms of a sequence. If the sequence is the expression is called the series associated with it. A series is represented by ‘S’ or the Greek symbol.

The series can be finite or infinte. Examples: 5 + 2 + (-1) + (-4) is a finite series obtained by subtracting 3 from the previous number.1/5. This monograph should be of interest to a broad spectrum of readers: specialists in discrete and continuous mathematics, physicists, engineers, and others interested in computing sums and applying complex analysis in discrete mathematics.

It contains investigations on the problem of finding integral representations for and computing finite and infinite sums (generating. No book of this type exists which attempts to give a link, by developing a comprehensive method, between non-hypergeometric and hypergeometric summation.

This book is intended for use in the fields of applied mathematics, analysis, non-hypergeometric and hypergeometric summation, summation of series and automated techniques."Price: $ Accordingly, numerical techniques for the acceleration of convergence or the summation of divergent series are almost as old as calculus itself.

According to Knopp M p. ], the first series transformation was published by Stirling [pi already inand in Euler [H published the series transformation which now bears his name.

Summation of a Series In Core Two we learned about arithmetic and geometric progression, but if we need to sum an arithmetic progression over a large range it can become very time consuming. There are formulae that can allow us to calculate the sum.

In Mathematics we have studied “SUMMATION“. the below example provides you the C++ code to find summation of several numbers in C++. We can take the inputs from the user to create a type of series and then find the summation, we just have to change the statement inside the for loop for the desired formula, but here we considered it for summation of even numbers from 1.

Valuable as text and a reference, this concise monograph covers calculus of finite differences, gamma and psi functions, other methods of summation, summation of tables, and infinite sums. edition. Category: Mathematics Computational Techniques For The Summation Of Series.

The NOOK Book (eBook) of the Computational Techniques for Process Simulation and Analysis Using MATLAB® by Niket S. Kaisare at Barnes & Noble. FREE B&N Outlet Membership Educators Gift Cards Stores & Events HelpPrice: $ summability methods.

Methods for constructing generalized sums of series, generalized limits of sequences, and values of improper integrals. In mathematical analysis, the need arises to generalize the concept of the sum of a series (limit of a sequence, value of an integral) to include the case where the series (sequence, integral) diverges in the ordinary sense.

This. Methods for the Summation of Infinite Series Article (PDF Available) in International Journal of Mathematics and Computer Science 11(2) November Author: Henrik Stenlund. Computational methods 4 Function calculation • Chapter 5.

– Calculation of power series – acceleration – Continued fractions • E.g. to calculate pi to a million decimals – Recurrence • when you need to accelerate calculations involving series, study the book.

I will only use the Chebyshev formalism in this course. The techniques that I can recall using in the past include: Using known power series expansions (including things like geometric series) Differentiating or integrating power series.

Using complex analysis (look for summation of series by using residues) as in this question. Fourier expansions, including Parseval's theorem - as in this question. The Summation of Series. Harold Thayer Davis. Principia Press of Trinity University, Jan 1, - Series - pages.

0 Reviews. Preview this book. Vectorization with Einstein summation notation; Comparison of EM routines; Monte Carlo Methods.

Pseudorandom number generators (PRNG) Monte Carlo swindles (Variance reduction techniques) Quasi-random numbers; Resampling methods. Resampling; Simulations; Setting the random seed; Sampling with and without replacement; Calculation of Cook’s distance. A series may also be represented by using summation notation, such as ∑ = ∞.

If an abelian group A of terms has a concept of limit (for example, if it is a metric space), then some series, the convergent series, can be interpreted as having a value in A, called the sum of the series. This includes the common cases from calculus in which the.

develop the summation formula previously mentioned, and then apply it to a few series, in particular, X1 n=1 1 n2 of Euler fame. We will conclude with an extension and variation of the summation formula.

2 The Residue Calculus The technique we will develop relies heavily on the Residue Theorem, so before considering any in nite series, let us brieFile Size: KB. A summation method is regular if, whenever the sequence s converges to x, A(s) = x. Equivalently, the corresponding series-summation method evaluates A Σ (a) = x.

Linearity. A is linear if it is a linear functional on the sequences where it is defined, so that A(k r + s) = k A(r) + A(s) for sequences r, s and a real or complex scalar k.

Such schemes are more expensive than simple truncation, but the advantage is that they respect the long-range character of the forces. The techniques include Ewald summation, fast multi-pole methods, and particle-mesh-based techniques. Of these, the Ewald summation is the most widely used technique.

Gradshteyn & Ryzhik’s Table of Integrals, Series, and Products is still being updated and, although primarily an integrals book, does have extensive sections on finite and infinite sums.

Another excellent table, although out-of-print today, is L. Jolley’s Summation of Series (Dover, 2 nd revised edition, ). From Reviews Of The Series "Reviews in Computational Chemistry remains the most valuable reference to methods and techniques in computational chemistry."-Journal Of Molecular Graphics And Modelling "One cannot generally do better than to try to find an appropriate article in the highly successful Reviews in Computational Chemistry.

The n-th partial sum of a series is the sum of the ﬁrst n terms. The sequence of partial sums of a series sometimes tends to a real limit. If this happens, we say that this limit is the sum of the series.

If not, we say that the series has no sum. A series can have a sum only if the individual terms tend to zero. But there are some series.

Convergence acceleration techniques. In M. Laudon, & B. Romanowicz (Eds.), Nanotechnology Conference and Trade Show - Nanotech (Vol. 2, pp. ) Convergence acceleration : Ulrich D.

Jentschura, Sergej V. Aksenov, Peter J. Mohr, Michael A. Savageau, Gerhard Soff. Engineering Mathematics with Examples and Applications provides a compact and concise primer in the field, starting with the foundations, and then gradually developing to the advanced level of mathematics that is necessary for all engineering disciplines.

Therefore, this book's aim is to help undergraduates rapidly develop the fundamental. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

Manipulating a Summation Series. Ask Question Asked 2 years always try to decompose the summation into simple addition form. If you decompose your summation into simple series addition form these summations.mathematical and computational tool, provided that this series is summable to a ﬁnite gen-eralized limit.

Of course, there remains the practically very important question how such a divergent series can be summed in an eﬀective and numerically reliable way. The most important summation techniques used by theoretical physicists are Borel sum-Cited by: 1.Computational techniques for the summation of series / by: Sofo, Anthony.

Published: () Summability theory and its applications by: Başar, Feyzi. Published: () Borel's methods of summability: theory and applications / by: Shawyer, Bruce.