標(biāo)題: Titlebook: Ramanujan’s Notebooks; Part I Bruce C. Berndt Book 1985 Springer Science+Business Media New York 1985 calculus.exponential function.transfo [打印本頁] 作者: 天真無邪 時間: 2025-3-21 19:41
書目名稱Ramanujan’s Notebooks影響因子(影響力)
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https://doi.org/10.1007/978-1-4612-1088-7calculus; exponential function; transformation作者: Anal-Canal 時間: 2025-3-22 12:47 作者: Panacea 時間: 2025-3-22 15:23 作者: Foam-Cells 時間: 2025-3-22 18:15
Magic Squares,r constructing certain rectangular arrays of natural numbers are given. Most of Ramanujan’s attention is devoted to constructing magic squares. A magic square is a square array of (usually distinct) natural numbers so that the sum of the numbers in each row, column, or diagonal is the same. In some 作者: 售穴 時間: 2025-3-22 21:49
Combinatorial Analysis and Series Inversions,s. Another primary theme in Chapter 3 revolves around series expansions of various types. However, the deepest and most interesting result in Chapter 3 is Entry 10, which separates the two main themes but which has some connections with the former. Entry 10 offers a highly general and potentially ve作者: 性學(xué)院 時間: 2025-3-23 03:01
Iterates of the Exponential Function and an Ingenious Formal Technique,ein the Bell numbers, single-variable Bell polynomials, and related topics are studied. Recall that the Bell numbers .(.), 0 ≤ . ≤ ∞, may be defined by They were first thoroughly studied in print by Bell [1], [2] approximately 25–30 years after Ramanujan had derived several of their properties in th作者: Motilin 時間: 2025-3-23 07:21
Eulerian Polynomials and Numbers, Bernoulli Numbers, and the Riemann Zeta-Function,rity pertain to Bernoulli numbers, Euler numbers, Eulerian polynomials and numbers, and the Riemann zeta-function. As is to be expected, most of these results are not new. The geneses of Ramanujan’s first published paper [4] (on Bernoulli numbers) and fourth published paper [7] (on sums connected wi作者: 神刊 時間: 2025-3-23 12:21
,Ramanujan’s Theory of Divergent Series,dare to base any proof on them.” This admonition would have been vehemently debated by Ramanujan. Much like Euler, Ramanujan employed divergent series in a variety of ways to establish a diversity of results, most of them valid but a few not so. Divergent series are copious throughout Ramanujan’s no作者: intuition 時間: 2025-3-23 14:15 作者: In-Situ 時間: 2025-3-23 19:35
Analogues of the Gamma Function,series and the logarithmic derivative ψ(.) of the gamma function. As might be expected, most of these results are very familiar. Ramanujan actually does not express his formulas in terms of ψ(.) but instead in terms of .. As in Chapter 6, Ramanujan really intends ?(.) to be interpreted as ?(. + 1) +作者: defray 時間: 2025-3-24 01:11
Infinite Series Identities, Transformations, and Evaluations,nite series, and so forth, that was most amazing.” This chapter has 35 sections containing 139 formulas of which many are, indeed, very beautiful and elegant. Ramanujan gives several transformations of power series leading to many striking series relations and attractive series evaluations. Most of 作者: 數(shù)量 時間: 2025-3-24 06:16
Iterates of the Exponential Function and an Ingenious Formal Technique,taken by Bell [2] in 1938. Becker and Riordan [1] and Carlitz [1] have established arithmetical properties for these generalizations of Bell numbers. Also, Ginsburg [1] has briefly considered such iterates. For a combinatorial interpretation of numbers generated by iterated exponential functions, see Stanley’s article [1, Theorem 6.1].作者: jeopardize 時間: 2025-3-24 10:17
,Ramanujan’s Theory of Divergent Series,ing identities that involve one or more divergent series, one might be led to believe that Ramanujan probably made no distinction between convergent and divergent series. However, the occasional discourse in Chapter 6 is firm evidence that Ramanujan made such a distinction.作者: 圖畫文字 時間: 2025-3-24 13:19 作者: 祝賀 時間: 2025-3-24 18:52 作者: ALOFT 時間: 2025-3-24 22:43
Analogues of the Gamma Function, γ, ., where γ denotes Euler’s constant. These 14 sections also contain several evaluations of elementary integrals of rational functions. Certain of these integrals are connected with an interesting series ., which Ramanujan also examined in Chapter 2.作者: 有權(quán) 時間: 2025-3-24 23:58 作者: 簡略 時間: 2025-3-25 03:46
Book 19850theorems, virtually all without proof. G.H. Hardy andothers strongly urged that notebooks be edited andpublished, and the result is this series of books. Thisvolume dealswith Chapters 1-9 of Book II; each theorem iseither proved, or a reference to a proof is given.作者: 脫離 時間: 2025-3-25 08:22 作者: 易受刺激 時間: 2025-3-25 11:53
Book 1985mathematics, hetaught himself, and managed to produce many important newresults. With the support of the English number theorist G.H.Hardy, Ramanujan received a scholarship to go to Englandand studymathematics. He died very young, at the age of 32,leaving behind three notebooks containing almost 300作者: 小隔間 時間: 2025-3-25 17:14
Introduction,ucation, the absence of books and journals, working in isolation in his most creative years, and an early death at the age of 32. Few, if any, of his mathematical peers had to encounter so many formidable obstacles.作者: Infantry 時間: 2025-3-25 23:26 作者: HEAVY 時間: 2025-3-26 00:21 作者: 拍翅 時間: 2025-3-26 04:44 作者: Palpate 時間: 2025-3-26 11:28
Bruce C. Berndt Sovereignty, Pet Food, and Stoicism.The most comprehensive,.The second edition of this extensive work is the definitive source on issues pertaining to the full range of topics in the important area of food and agricultural ethics.?Altogether about?.100 new entries.?appear in this new edition.?The s作者: 等待 時間: 2025-3-26 12:55 作者: 惡名聲 時間: 2025-3-26 20:01 作者: 反復(fù)無常 時間: 2025-3-26 22:56 作者: Corporeal 時間: 2025-3-27 03:32 作者: 獎牌 時間: 2025-3-27 06:07
Bruce C. Berndtstandards.Provides a comprehensive and authoritative treatme.New In This Edition:. This second edition of the Encyclopedia of GIS includes 30% to 50% new content. It provides up-to-date information on emerging topics such as spatial big data, smart-phone GIS, urban computing and mobile recommender s作者: Keratin 時間: 2025-3-27 12:34 作者: 軌道 時間: 2025-3-27 14:54 作者: 共和國 時間: 2025-3-27 21:44 作者: MOCK 時間: 2025-3-28 00:55 作者: 拍翅 時間: 2025-3-28 05:37 作者: 白楊 時間: 2025-3-28 08:54
organic farming, Islam and Food, and cannibalism.The .Encyclopedia of Food and Agricultural Ethics,?.2.nd?.edition?is an indispensable reference point for future research and writing on topics in agriculture, food, animal, and eating ethics..978-94-024-1179-9作者: Kaleidoscope 時間: 2025-3-28 10:30
Bruce C. Berndtorganic farming, Islam and Food, and cannibalism.The .Encyclopedia of Food and Agricultural Ethics,?.2.nd?.edition?is an indispensable reference point for future research and writing on topics in agriculture, food, animal, and eating ethics..978-94-024-1179-9作者: 不近人情 時間: 2025-3-28 15:51 作者: Expediency 時間: 2025-3-28 20:19 作者: 徹底明白 時間: 2025-3-29 00:37 作者: 誘惑 時間: 2025-3-29 05:06
Bruce C. Berndt content and intuitive A-Z organization, this new edition of the encyclopedia is an invaluable reference for newcomers to the field of?GIS, as well as researchers, students, developers and professionals who are978-3-319-23519-6作者: DEFER 時間: 2025-3-29 07:30
Bruce C. Berndt content and intuitive A-Z organization, this new edition of the encyclopedia is an invaluable reference for newcomers to the field of?GIS, as well as researchers, students, developers and professionals who are978-3-319-23519-6
