ON SEMISIMPLE LIE ALGEBRAS AND SPECIAL FUNCTIONS
Medhat Ahmed Ibrahim Rakha;
Abstract
The main point of the scope of this thesis is to establish and prove two new q-beta integrals and two multivariate basic hypergeometric series associated to the root system of the classical Lie algebra A,., at the same time to give a generalization of Jackson's well-poised s'i'7 sum for one kind of the series and a generalization of the q-G.,.uss sum for the other kind of the series.
The present thesis is divided into six chapters :
• The first chapter presents the basic and necessary definitions in both Lie algebras and hypergeometric series, also we give a brief description of the main results of this thesis.
• In the second chapter, a historical background materials of the main research point in this thesis is given.
• The third chapter is devoted to the evaluation of the main integral for the classical Lie algebra Am .
• In the fourth chapter we study and prove the convergence of the cor responding basic hypergeometric series associated to the main integral presented in chapter three, also we discuss the different types of poles of the integrand of the main integral.
• In chapter five, we prove the series identities for the main integral in both the even and odd cases and prove a general summation theorem which extends the classical Jackson well-poised 8 1]!7 summation theo rem.
• In the last chapter we evaluate some selected series, that extend the classical q-Gauss summation theorem.
The present thesis is divided into six chapters :
• The first chapter presents the basic and necessary definitions in both Lie algebras and hypergeometric series, also we give a brief description of the main results of this thesis.
• In the second chapter, a historical background materials of the main research point in this thesis is given.
• The third chapter is devoted to the evaluation of the main integral for the classical Lie algebra Am .
• In the fourth chapter we study and prove the convergence of the cor responding basic hypergeometric series associated to the main integral presented in chapter three, also we discuss the different types of poles of the integrand of the main integral.
• In chapter five, we prove the series identities for the main integral in both the even and odd cases and prove a general summation theorem which extends the classical Jackson well-poised 8 1]!7 summation theo rem.
• In the last chapter we evaluate some selected series, that extend the classical q-Gauss summation theorem.
Other data
| Title | ON SEMISIMPLE LIE ALGEBRAS AND SPECIAL FUNCTIONS | Other Titles | حول حبريات لى شبه البسيطة والدوال الخاصة | Authors | Medhat Ahmed Ibrahim Rakha | Issue Date | 1998 |
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