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Bases of special functions and their domains of convergence

Author: Josef Saurer
Publisher: Berlin : Akademie Verlag GmbH, ©1993.
Series: Mathematical research, Bd. 73.
Edition/Format:   Print book : English : 1st edView all editions and formats
Database:WorldCat
Summary:

This text presents a systematic approach to expansions of analytic functions in series of special functions. Many expansions of this kind are identified, with eigenfunction expansions for  Read more...

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Additional Physical Format: Online version:
Saurer, Josef, 1965-
Bases of special functions and their domains of convergence.
Berlin : Akademie Verlag GmbH, ©1993
(OCoLC)622952935
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Josef Saurer
ISBN: 3055016130 9783055016134
OCLC Number: 28938024
Notes: Revision of the author's thesis--Universität Essen, 1992.
Description: 158 pages : illustrations ; 24 cm.
Contents: 1. Foundations of the theory. 1.1. Holomorphic operator functions in Frechet spaces. 1.2. Floquet eigenvalue problems (with a regular singular point). 1.3. Relationships between differential operators corresponding to Floquet eigenvalue problems for systems of differential equations and scalar differential equations. 1.4. Biholomorphic images of functions. 1.5. An expansion theorem --
2. First order differential systems with a regular singular point. 2.1. Fundamental properties. 2.2. Construction of fundamental systems depending holomorphically on parameters. 2.3. A family of second order differential equations. 2.4. Differential equations and special functions of mathematical physics. 2.4.1. Bessel equation, Bessel function. 2.4.2. Whittaker equation, Whittaker function. 2.4.3. Hypergeometric equation, hypergeometric function. 2.4.4. Generalised spherical function --
3. Floquet eigenvalue problems for first order differential systems with a regular singular point. 3.1. Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions T and T[superscript *]. 3.2. A general expansion theorem. 3.3. Floquet eigenvalue problems and expansion theorems for a family of second order differential equations --
4. Domains of convergence of the eigenfunction expansions. 4.1. The Bessel and Whittaker case. 4.2. The hypergeometric case. 4.3. Typical domains of convergence --
5. Examples of expansions in series of special functions. 5.1. Expansions in series of Bessel functions. 5.2. Expansions in series of Whittaker functions. 5.3. Expansions in series of hypergeometric functions --
6. First order differential systems for products of vector-valued functions. 6.1. Products of vectors and sums of matrices of different dimensions. 6.2. Construction of the first order differential system --
7. Floquet eigenvalue problems and expansions in series, of m --
fold products of special functions. 7.1. Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions T and T[superscript *]. 7.2. Application.
Series Title: Mathematical research, Bd. 73.
Responsibility: Josef Saurer.

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