Polygamma Functions

In this chapter, we introduce the digamma function, which is the logarithmic derivative of the gamma function, and its derivatives (Sect. 2.1). These functions have remarkable series expansions (Sect. 2.2) and lead to Bernoulli and Euler numbers (Sect. 2.3). They also allow to obtain the asymptotic expansion of the gamma function by using Laplace transform (Sect. 2.4) and are connected with the zeta (Sect. 2.5) and polylogarithm (Chap. 8 ) functions. However, the results of this chapter will be used only for the study of polylogarithm functions (Chap. 8 ) and not in the other chapters.