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• catalog contributor b5029388.
• catalog date "1993".
• catalog description "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.".
• catalog description "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.".
• catalog description "7.1. Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions T and T[superscript *]. 7.2. Application.".
• catalog description "Includes bibliographical references (p. [151]-153) and index.".
• catalog description "Thesis--Universität Essen, 1992.".
• catalog extent "158 p. :".
• catalog hasFormat "Bases of special functions and their domains of convergence.".
• catalog identifier "3055016130".
• catalog isFormatOf "Bases of special functions and their domains of convergence.".
• catalog isPartOf "Mathematical research ; v. 73".
• catalog issued "1993".
• catalog language "eng".
• catalog relation "Bases of special functions and their domains of convergence.".
• catalog subject "Analytic functions.".
• catalog subject "Convergence.".
• catalog subject "Eigenfunction expansions.".
• catalog subject "Functions, Special.".
• catalog subject "Mathematical physics.".
• catalog subject "QA351 .S28 1993".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog tableOfContents "7.1. Construction of biorthogonal canonical systems of eigen- and associated vectors of the operator functions T and T[superscript *]. 7.2. Application.".
• catalog title "Bases of special functions and their domains of convergence / Josef Saurer.".
• catalog type "text".