Download pdf Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint)
Download pdf Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint)
Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint).cCharles H Chapman
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Author: Charles H Chapman
Number of Pages: 46 pages
Published Date: 27 Sep 2015
Publisher: Forgotten Books
Publication Country: United States
Language: English
ISBN: 9781330112687
File Name: Thesis.Riemann's.P-Function.Dissertation.Presented.for.the.Degree.of.Doctor.of.Philosophy.in.the.Johns.Hopkins.University.(Classic.Reprint).pdf
Download Link: Thesis Riemann's P-Function Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint)
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Excerpt from Thesis Riemann's P-Function: Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University The following paper was begun at the suggestion of Dr. Craig and has had the benefit of his advice and criticism. It is an attempt to set forth in a clear and readable form the properties of the P-function invented by Riemann and treated of in his collected works. Part I of the present paper is devoted to a restatement in systematic order of the properties of the function as given by Riemann, with full demonstrations of certain points at which he has only hinted, and original proofs of some propositions which he considered almost self-evident, but which admit, and perhaps require, elaborate demonstrations. Section 4 of Part I is an instance of this kind; the work therein and the table of equivalent functions are my own. The same may be said of Section 6, where, by using an expansion in powers of the variable which is known to be convergent in the proper regions, the ideas are fixed and a certain ease of statement is attained. In proving that the P-function satisfies a linear differential equation of the second order I have followed Riemann, except that certain points in the Theory of Functions have been touched more lightly, as being better known to readers at the present day. Part II is entirely my own. It is a study of the differential equation satisfied by the P-function from the point of view of the modern theory as originated by Fuchs and developed by his illustrious collaborators.Section 5 is devoted to obtaining the coefficients of the differential equation; and in subsequent sections the Spherical Harmonics, Toroidal functions and Bessel's functions are expressed as P-functions, while, in conclusion, the P-function itself is expressed as a Hypergeometric Series. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Read online Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint) Buy Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint) Download and read Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint) for pc, mac, kindle, readers Download to iPad/iPhone/iOS, B&N nook Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint) ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent
Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint).cCharles H Chapman
Author: Charles H Chapman
Number of Pages: 46 pages
Published Date: 27 Sep 2015
Publisher: Forgotten Books
Publication Country: United States
Language: English
ISBN: 9781330112687
File Name: Thesis.Riemann's.P-Function.Dissertation.Presented.for.the.Degree.of.Doctor.of.Philosophy.in.the.Johns.Hopkins.University.(Classic.Reprint).pdf
Download Link: Thesis Riemann's P-Function Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint)
---------------------------------------------------------------
Excerpt from Thesis Riemann's P-Function: Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University The following paper was begun at the suggestion of Dr. Craig and has had the benefit of his advice and criticism. It is an attempt to set forth in a clear and readable form the properties of the P-function invented by Riemann and treated of in his collected works. Part I of the present paper is devoted to a restatement in systematic order of the properties of the function as given by Riemann, with full demonstrations of certain points at which he has only hinted, and original proofs of some propositions which he considered almost self-evident, but which admit, and perhaps require, elaborate demonstrations. Section 4 of Part I is an instance of this kind; the work therein and the table of equivalent functions are my own. The same may be said of Section 6, where, by using an expansion in powers of the variable which is known to be convergent in the proper regions, the ideas are fixed and a certain ease of statement is attained. In proving that the P-function satisfies a linear differential equation of the second order I have followed Riemann, except that certain points in the Theory of Functions have been touched more lightly, as being better known to readers at the present day. Part II is entirely my own. It is a study of the differential equation satisfied by the P-function from the point of view of the modern theory as originated by Fuchs and developed by his illustrious collaborators.Section 5 is devoted to obtaining the coefficients of the differential equation; and in subsequent sections the Spherical Harmonics, Toroidal functions and Bessel's functions are expressed as P-functions, while, in conclusion, the P-function itself is expressed as a Hypergeometric Series. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Read online Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint) Buy Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint) Download and read Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint) for pc, mac, kindle, readers Download to iPad/iPhone/iOS, B&N nook Thesis Riemann's P-Function : Dissertation Presented for the Degree of Doctor of Philosophy in the Johns Hopkins University (Classic Reprint) ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent