8–9 - Special Functions

Abstract

This chapter discusses elliptic integrals and functions, the exponential integral function and functions generated by them, Euler's integrals of the first and second kinds and the functions generated by them, Bessel functions and functions associated with them, along with a series of Bessel functions. It also describes Mathieu functions, associated Legendre functions, orthogonal polynomials, hypergeometric functions, confluent hypergeometric functions, Meijer's G-function, MacRobert's E-function, Riemann's zeta functions and the functions Φ and ξ, Bernoulli numbers and polynomials, and Euler numbers polynomials. The Euler numbers are integers and the Euler numbers of odd index are equal to zero; the signs of two adjacent numbers of even indices are opposite.