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The Theory of Residues; Application to the Evaluation of Definite Integrals 残数理论;在定积分求值中的应用
A Course of Modern Analysis Pub Date : 2021-08-31 DOI: 10.1017/9781009004091.014
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引用次数: 0
The Equations of Mathematical Physics 数学物理方程
A Course of Modern Analysis Pub Date : 2021-08-31 DOI: 10.1017/9781009004091.027
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引用次数: 0
The Expansion of Functions in Infinite Series 无穷级数中函数的展开
A Course of Modern Analysis Pub Date : 2021-08-31 DOI: 10.1017/9781009004091.015
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引用次数: 0
Elliptic Functions. General Theorems and the Weierstrassian Functions 椭圆函数。一般定理与Weierstrassian函数
A Course of Modern Analysis Pub Date : 2021-08-31 DOI: 10.1017/9781009004091.029
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引用次数: 0
The Fundamental Properties of Analytic Functions; Taylor’s, Laurent’s and Liouville’s Theorems 解析函数的基本性质泰勒定理，劳伦定理和刘维尔定理
A Course of Modern Analysis Pub Date : 2021-08-31 DOI: 10.1017/9781009004091.013
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引用次数: 0
Fourier Series and Trigonometric Series 傅里叶级数和三角级数
A Course of Modern Analysis Pub Date : 2021-08-31 DOI: 10.1017/9781009004091.017
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引用次数: 0
Mathieu Functions 马修功能
A Course of Modern Analysis Pub Date : 2021-08-31 DOI: 10.1017/cbo9780511608759.020
E. T. Whittaker, G. Watson
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引用次数: 11
Complex Numbers 复数
A Course of Modern Analysis Pub Date : 2021-08-31 DOI: 10.1017/9781009004091.009
Viola Maria Grazia
{"title":"Complex Numbers","authors":"Viola Maria Grazia","doi":"10.1017/9781009004091.009","DOIUrl":"https://doi.org/10.1017/9781009004091.009","url":null,"abstract":"In this article we study the complexes in an other point of view. Definition The Complex field is defined like IR/(x+1) we assume, like all know, i ≔ sqrt{−1} And we view complexes like IR(i) Now, we know that the complex numbers are rapresented on the plane but it is only the graph of the vectorial space of the complexes in other word they can be rapresented in the following way We take a point in the real plane with polar coordinate pcosO i + psinO j , where p is positive real number and O is in [0,2pi[ And know that if we moltiplicate a complex ‘A’ with i, ‘A’ will rotate by an angle of pi/2 anticlockwise So our point in real plane becomes the complex point (pcosO-ipsinO)i We note that the complexes are all on the complex straight line y=0 We saw also that (-i,0),(i,0) is the solution of the system y=0 && y=x+1 (-2i,0),(2i,0) is the solution of the system y=0 && y = x+4 (-i+1,0),(i+1,0)is the solution of the system y=0 && y=(x-1)+1 etc etc So the some complexes are rapresented on the line like this ... -1+i -1 0 -i -2i -3i ... 3i 2i i 0 1 1-i 1-2i 1+i 1 2 2-i Pi Pi-i ... The position of -i ad i etc etc depends by the rotation and the rapresentation of real plane in this the author keep the same direction of the angles i.e. anticlockwise.","PeriodicalId":125547,"journal":{"name":"A Course of Modern Analysis","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125993217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Hypergeometric Function 超几何函数
A Course of Modern Analysis Pub Date : 2021-08-31 DOI: 10.1201/9781439864548-61
Moseley Typist, E. Peters
{"title":"The Hypergeometric Function","authors":"Moseley Typist, E. Peters","doi":"10.1201/9781439864548-61","DOIUrl":"https://doi.org/10.1201/9781439864548-61","url":null,"abstract":"Notes from the “Conformal Field Theory and Operator Algebras workshop,” August 2010, Oregon. Want to relate Fμ and Gμ after analytic continuation. Writing Fμs in terms of Gνs – coefficients are ”transport coefficients.” (1) Hypergeometric function/equation (2) Compute transport coefficients for the “Basic ODE” Definition. Gauss’s hypergeometric equation: second order ODE with 3 regular singular points {0, 1,∞}: z(1− z)f ′′ + [c− (1 + a+ b)z]f ′ − abf = 0. What’s cool about this are its solutions, built from 2F1 (a, b; c; z) = Σn≥0 (a)n(b)n (c)n z n! with (a)n := a(a+ 1) · · · (a+ n− 1). Rewrite differential equation as F (z) = ( A z + B 1− z )F (z)","PeriodicalId":125547,"journal":{"name":"A Course of Modern Analysis","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124162184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Confluent Hypergeometric Function 合流超几何函数
A Course of Modern Analysis Pub Date : 2021-08-31 DOI: 10.1017/9781009004091.025
{"title":"The Confluent Hypergeometric Function","authors":"","doi":"10.1017/9781009004091.025","DOIUrl":"https://doi.org/10.1017/9781009004091.025","url":null,"abstract":"","PeriodicalId":125547,"journal":{"name":"A Course of Modern Analysis","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116007604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 176
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