Methods for the Summation of Series

Methods for the Summation of Series
Author: Tian-Xiao He
Publisher: CRC Press
Total Pages: 458
Release: 2022-01-26
Genre: Mathematics
ISBN: 1000534332

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This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding. Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.

Computational Techniques for the Summation of Series

Computational Techniques for the Summation of Series
Author: Anthony Sofo
Publisher: Springer Science & Business Media
Total Pages: 194
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461500575

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"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." --The Australian Mathematical Society Gazette

The Summation of Series

The Summation of Series
Author: Harold Thayer Davis
Publisher:
Total Pages: 158
Release: 1962
Genre: Mathematics
ISBN:

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Methods for the Summation of Series

Methods for the Summation of Series
Author: Tian-Xiao He
Publisher: CRC Press
Total Pages: 301
Release: 2022-01-26
Genre: Mathematics
ISBN: 1000534375

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This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding. Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.

The Summation of Series

The Summation of Series
Author: Harold T. Davis
Publisher: Courier Corporation
Total Pages: 164
Release: 2015-02-18
Genre: Mathematics
ISBN: 0486789683

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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. 1962 edition.

Ramanujan Summation of Divergent Series

Ramanujan Summation of Divergent Series
Author: Bernard Candelpergher
Publisher: Springer
Total Pages: 211
Release: 2017-09-12
Genre: Mathematics
ISBN: 3319636308

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The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.

Sum

Sum
Author: David Eagleman
Publisher: Vintage
Total Pages: 128
Release: 2009-02-10
Genre: Fiction
ISBN: 0307378020

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At once funny, wistful and unsettling, Sum is a dazzling exploration of unexpected afterlives—each presented as a vignette that offers a stunning lens through which to see ourselves in the here and now. In one afterlife, you may find that God is the size of a microbe and unaware of your existence. In another version, you work as a background character in other people’s dreams. Or you may find that God is a married couple, or that the universe is running backward, or that you are forced to live out your afterlife with annoying versions of who you could have been. With a probing imagination and deep understanding of the human condition, acclaimed neuroscientist David Eagleman offers wonderfully imagined tales that shine a brilliant light on the here and now.

The Runelords

The Runelords
Author: David Farland
Publisher: Tor Fantasy
Total Pages: 625
Release: 2007-04-01
Genre: Fiction
ISBN: 1429911964

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The first book of the saga of The Runelords Young Prince Gaborn Val Orden of Mystarria is traveling in disguise on a journey to ask for the hand of the lovely Princess Iome of Sylvarresta. Armed with his gifts of strength and perception, Prince Gaborn and his warrior bodyguard stop in a local tavern along the way. Immediately, they spot a pair of assassins who have their sights set on Princess Iome's father. As the prince and his bodyguard race to warn the king of this impending danger, they realize that more than the royal family is at risk, the very fate of the Earth is in jeopardy. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.

The Sum of Trifles

The Sum of Trifles
Author: Julia Ridley Smith
Publisher: University of Georgia Press
Total Pages: 254
Release: 2021-11-01
Genre: Biography & Autobiography
ISBN: 0820360422

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When Julia Ridley Smith’s parents died, they left behind a virtual museum of furniture, books, art, and artifacts. Between the contents of their home, the stock from their North Carolina antiques shop, and the ephemera of two lives lived, Smith faced a monumental task. What would she do with her parents’ possessions? Smith’s wise and moving memoir in essays, The Sum of Trifles, peels back the layers of meaning surrounding specific objects her parents owned, from an eighteenth-century miniature to her father’s prosthetics. A vintage hi-fi provides a view of her often tense relationship with her father, whose love of jazz kindled her own artistic impulse. A Japanese screen embodies her mother’s principles of good taste and good manners, while an antebellum quilt prompts Smith to grapple with her family’s slaveholding legacy. Along the way, she turns to literature that illuminates how her inheritance shaped her notions of identity and purpose. The Sum of Trifles offers up dark humor and raw feeling, mixed with an erudite streak. It’s a curious, thoughtful look at how we live in and with our material culture and how we face our losses as we decide what to keep and what to let go.

The Sum of Us

The Sum of Us
Author: Heather McGhee
Publisher: One World
Total Pages: 450
Release: 2021-02-16
Genre: Social Science
ISBN: 0525509577

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NEW YORK TIMES BESTSELLER • LONGLISTED FOR THE NATIONAL BOOK AWARD • One of today’s most insightful and influential thinkers offers a powerful exploration of inequality and the lesson that generations of Americans have failed to learn: Racism has a cost for everyone—not just for people of color. WINNER OF THE PORCHLIGHT BUSINESS BOOK AWARD • ONE OF THE BEST BOOKS OF THE YEAR: Time, The Washington Post, St. Louis Post-Dispatch, Ms. magazine, BookRiot, Library Journal “This is the book I’ve been waiting for.”—Ibram X. Kendi, #1 New York Times bestselling author of How to Be an Antiracist Look for the author’s new podcast, The Sum of Us, based on this book! Heather McGhee’s specialty is the American economy—and the mystery of why it so often fails the American public. From the financial crisis of 2008 to rising student debt to collapsing public infrastructure, she found a root problem: racism in our politics and policymaking. But not just in the most obvious indignities for people of color. Racism has costs for white people, too. It is the common denominator of our most vexing public problems, the core dysfunction of our democracy and constitutive of the spiritual and moral crises that grip us all. But how did this happen? And is there a way out? McGhee embarks on a deeply personal journey across the country from Maine to Mississippi to California, tallying what we lose when we buy into the zero-sum paradigm—the idea that progress for some of us must come at the expense of others. Along the way, she meets white people who confide in her about losing their homes, their dreams, and their shot at better jobs to the toxic mix of American racism and greed. This is the story of how public goods in this country—from parks and pools to functioning schools—have become private luxuries; of how unions collapsed, wages stagnated, and inequality increased; and of how this country, unique among the world’s advanced economies, has thwarted universal healthcare. But in unlikely places of worship and work, McGhee finds proof of what she calls the Solidarity Dividend: the benefits we gain when people come together across race to accomplish what we simply can’t do on our own. The Sum of Us is not only a brilliant analysis of how we arrived here but also a heartfelt message, delivered with startling empathy, from a black woman to a multiracial America. It leaves us with a new vision for a future in which we finally realize that life can be more than a zero-sum game. LONGLISTED FOR THE ANDREW CARNEGIE MEDAL