Author: John Edward Weidlich
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 144
Book Description
Summability Methods for Divergent Series
Author: John Edward Weidlich
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 144
Book Description
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 144
Book Description
Summability Methods of Certain Divergent Series
Author: Billy Ray Sneed
Publisher:
ISBN:
Category :
Languages : en
Pages : 56
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 56
Book Description
Summability Methods for Divergent Series
Author: Jackie B. Garner
Publisher:
ISBN:
Category :
Languages : en
Pages : 114
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 114
Book Description
Summability Methods of Divergent Series
Author: Luigina Sandra Cianfarani Sogliero
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 68
Book Description
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 68
Book Description
On the Summability Methods of Divergent Series
Author: Kauzo Ishiguro
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 1054
Book Description
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 1054
Book Description
On the Summability Methods of Divergent Series
Author: Kazuo Ishiguro
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 0
Book Description
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 0
Book Description
Divergent Series, Summability and Resurgence I
Author: Claude Mitschi
Publisher: Springer
ISBN: 3319287362
Category : Mathematics
Languages : en
Pages : 314
Book Description
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.
Publisher: Springer
ISBN: 3319287362
Category : Mathematics
Languages : en
Pages : 314
Book Description
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.
Ramanujan Summation of Divergent Series
Author: Bernard Candelpergher
Publisher: Springer
ISBN: 3319636308
Category : Mathematics
Languages : en
Pages : 211
Book Description
The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.
Publisher: Springer
ISBN: 3319636308
Category : Mathematics
Languages : en
Pages : 211
Book Description
The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.
Divergent Series, Summability and Resurgence III
Author: Eric Delabaere
Publisher: Springer
ISBN: 3319290002
Category : Mathematics
Languages : en
Pages : 252
Book Description
The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called “bridge equation”, which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1.
Publisher: Springer
ISBN: 3319290002
Category : Mathematics
Languages : en
Pages : 252
Book Description
The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called “bridge equation”, which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1.
On Methods of Summability of Divergent Series
Author: Marcelle Mattie Walker
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 48
Book Description
Publisher:
ISBN:
Category : Divergent series
Languages : en
Pages : 48
Book Description