Special functions and applications

This study consist of seven chapters.In the first chapter, it is generally mentioned about context, application areas and historical evolution of special function.In the second chapter, inner product, orhogonality and their definition, some examples are given.In the third chapter, via technical literature definitions and the features of the Legendre Function, Legendre Polinomial, Rodrigues Formula and Genereting Function are explained.In the fourth chapter, with the technical literature definitions and the features of the Bessel Function and Gamma Function is indicated.In the fifth chapter, the definition of the Chebyshev Function and Polynomial is defined.In the sixth chapter, after answering the question of ? Why is orthogonality needed??, eigenvalue, eigenvector through Sturm Lioville theory are explined.Finally, the last chapter covers the mathematical and numerical calculation and applications of orthogonal polynomial.