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Studies On Divergent Series And Summability And The Asymptotic Developments Of Functions Defined By Maclaurin Series


Author : Walter Burton Ford
language : en
Publisher: American Mathematical Soc.
Release Date : 1960


Download Studies On Divergent Series And Summability And The Asymptotic Developments Of Functions Defined By Maclaurin Series written by Walter Burton Ford and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Mathematics categories.


This book is based on several courses taught by the author at the University of Michigan between 1908 and 1912. It covers two main topics: asymptotic series and the theory of summability. The discussion of nowhere convergent asymptotic series includes the so-called MacLaurent summation formula, determining asymptotic expansions of various classes of functions, and the study of asymptotic solutions of linear ordinary differential equations. On the second topic, the author discusses various approaches to the summability of divergent series and considers in detail applications to Fourier series.

Studies On Divergent Series And Summability And The Asymptotic Developments Of Functions Defined By Maclaurin Series


Author : Walter Burton Ford
language : en
Publisher: American Mathematical Soc.
Release Date : 1960


Download Studies On Divergent Series And Summability And The Asymptotic Developments Of Functions Defined By Maclaurin Series written by Walter Burton Ford and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Mathematics categories.


This book is based on several courses taught by the author at the University of Michigan between 1908 and 1912. It covers two main topics: asymptotic series and the theory of summability. The discussion of nowhere convergent asymptotic series includes the so-called MacLaurent summation formula, determining asymptotic expansions of various classes of functions, and the study of asymptotic solutions of linear ordinary differential equations. On the second topic, the author discusses various approaches to the summability of divergent series and considers in detail applications to Fourier series.

Studies On Divergent Series And Summability And The Asymptotic Developments Of Functions Defined By Maclaurin Series


Author : Walter Burton Ford
language : en
Publisher: American Mathematical Soc.
Release Date : 1960


Download Studies On Divergent Series And Summability And The Asymptotic Developments Of Functions Defined By Maclaurin Series written by Walter Burton Ford and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Mathematics categories.


This book is based on several courses taught by the author at the University of Michigan between 1908 and 1912. It covers two main topics: asymptotic series and the theory of summability. The discussion of nowhere convergent asymptotic series includes the so-called MacLaurent summation formula, determining asymptotic expansions of various classes of functions, and the study of asymptotic solutions of linear ordinary differential equations. On the second topic, the author discusses various approaches to the summability of divergent series and considers in detail applications to Fourier series.

Studies On Divergent Series And Summability And The Asymptotic Developments Of Functions Defined By Maclaurin Series Asymptoti


Author : Walter Burton Ford
language : en
Publisher:
Release Date : 1960


Download Studies On Divergent Series And Summability And The Asymptotic Developments Of Functions Defined By Maclaurin Series Asymptoti written by Walter Burton Ford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Divergent series categories.




Calculus Of Finite Differences


Author : Charles Jordan
language : en
Publisher: American Mathematical Soc.
Release Date : 1965


Download Calculus Of Finite Differences written by Charles Jordan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Mathematics categories.




The Riemann Hypothesis And The Roots Of The Riemann Zeta Function


Author : Samuel W. Gilbert
language : en
Publisher: Riemann hypothesis
Release Date : 2009-01-01


Download The Riemann Hypothesis And The Roots Of The Riemann Zeta Function written by Samuel W. Gilbert and has been published by Riemann hypothesis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Mathematics categories.


The author demonstrates that the Dirichlet series representation of the Riemann zeta function converges geometrically at the roots in the critical strip. The Dirichlet series parts of the Riemann zeta function diverge everywhere in the critical strip. It has therefore been assumed for at least 150 years that the Dirichlet series representation of the zeta function is useless for characterization of the non-trivial roots. The author shows that this assumption is completely wrong. Reduced, or simplified, asymptotic expansions for the terms of the zeta function series parts are equated algebraically with reduced asymptotic expansions for the terms of the zeta function series parts with reflected argument, constraining the real parts of the roots of both functions to the critical line. Hence, the Riemann hypothesis is correct. Formulae are derived and solved numerically, yielding highly accurate values of the imaginary parts of the roots of the zeta function.

Formal Power Series And Linear Systems Of Meromorphic Ordinary Differential Equations


Author : Werner Balser
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-19


Download Formal Power Series And Linear Systems Of Meromorphic Ordinary Differential Equations written by Werner Balser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-19 with Mathematics categories.


Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.