The Logarithmic Integral Volume 1 [Paperback]

Self-contained study of real and complex analysis bringing together many separate parts of this subject.The theme of this unique work, the logarithmic integral, lies athwart much of twentieth century analysis. It is a thread connecting many apparently separate parts of the subject, and so is a natural point at which to begin a serious study of real and complex analysis. Professor Koosis' aim is to show how, from simple ideas, one can build up an investigation which explains and clarifies many different, seemingly unrelated problems; to show, in effect, how mathematics grows.This, the first of two volumes, is self-contained, but more importantly, by following the theme, Professor Koosis has produced a work that can be read as a whole. He has brought together here many results, some unpublished, some new, and some available only in inaccessible journals.The theme of this unique work, the logarithmic integral, lies athwart much of twentieth century analysis. It is a thread connecting many apparently separate parts of the subject, and so is a natural point at which to begin a serious study of real and complex analysis. Professor Koosis' aim is to show how, from simple ideas, one can build up an investigation which explains and clarifies many different, seemingly unrelated problems; to show, in effect, how mathematics grows.This, the first of two volumes, is self-contained, but more importantly, by following the theme, Professor Koosis has produced a work that can be read as a whole. He has brought together here many results, some unpublished, some new, and some available only in inaccessible journals.The theme of this unique work, the logarithmic integral, lies athwart much of twentieth century analysis. It is a thread connecting many apparently separate parts of the subject, and is a natural point at which to begin a serious study of real and complex analysis. Professor Koosis' aim is to show how, from simple ideas, one can build up an investigation that explains and clS2