Overview

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.

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9783319636290

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A well-researched study that is part biography of Kurosawa, part cultural history of modern Japan and part film monograph. Energetic, straightforward, and free of academic jargon. -- New York Times Book Review A prismatic look at the esteemed filmmaker's life. A sensitive investigation...Anderer also traces other dark forces in Kurosawa's life and 'the hollowed-out emptiness' of postwar Japan. Perceptive insights about the mysterious heart of a legendary movie and its maker. -- Kirkus Reviews Rashomon has become 'a key word of our time,' referring to the impossibility of knowing the truth and instead being confronted with multiple perceptions of what might have happened. Anderer turns that Rashomon effect on the film itself, presenting the inspirations and histories that went into its creation, including the pivotal consequences of the youthful double suicide of -Kurosawa's beloved older brother and his lover, writer Ryunosuke Akutagawa's original texts, Japanese film history, Kurosawa's films before and after, important collaborators' reminiscences, and much more. -- Library Journal Paul Anderer offers us not only the spiritual, philosophical, and aesthetic evolution of one of the pre-eminent masters of world cinema but a close insightful analysis of his most seminal and influential film. Lucid, knowing and elegantly nuanced, Kurosawa's Rashomon is a pivotal read not only for film makers and film scholars but for anyone who is simply enraptured by the masterworks of this giant of twentieth century culture. -- Richard Price, author of 'The Whites and Lush Life' A powerful and deeply engrossing account of one of the greatest artists-and greatest films-of modern times. Paul Anderer, who wears his learning lightly, deftly brings to life Kurosawa's world, work, and influences. This is cultural history at its very best. -- James Shapiro, author of 'The Year of Lear: Shakespeare in 1606' Paul Anderer takes an altogether fresh look at Kurosawa's most famous film, finding its deep wellsprings in catastrophes both public and private. His book gives a rich sense of the turbulent modernist currents and formidable pre-war film culture that nurtured Kurosawa's art, and movingly conveys just how much was at stake in every frame of his greatest works. -- Geoffrey O'Brien, author of 'Stolen Glimpses'

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