SPECIAL FUNCTIONS AND THEIR APPLICATIONS

Abstract

This report deals with a branch of mathematics of utmost importance to scientists and engineers concerned with actual mathematical calculations. This further deals with the basic theory of some special functions, as well as applications of this theory to specific problems of physics and engineering. In the choice of topics, we have been guided by the goal of giving a sufficiently detailed exposition of those problems which are of greatest practical interest. Beginning with the basic function and their properties like BETA FUNCTIONS, GAMMA FUNC TIONS and HYPERGEOMETRIC FUNCTIONS, further exploring special functions including CYLIN DRICAL and SPHERICAL FUNCTIONS. Chapters containing BESSELS AND LEGENDERS FUNCTIONS are described according to their different types along with their important properties. Certain applications of these functions in math ematics and physics are used to convey the importance of these functions in various fields. Also solved examples would help in the implication of these formulas derived, in the real world. The text is also supported with few graphs of the above-mentioned function to provide a good visual representation along with the study of these special functions. Finally, the references have been brought up-to-date.