# §25.1 Special Notation

(For other notation see Notation for the Special Functions.)

$k,m,n$ nonnegative integers. prime number. real variable. real or complex parameter. complex variable. complex variable. Euler’s constant (§5.2(ii)). digamma function $\Gamma'\left(x\right)/\Gamma\left(x\right)$ except in §25.16. See §5.2(i). Bernoulli number and polynomial (§24.2(i)). periodic Bernoulli function $B_{n}\left(x-\left\lfloor x\right\rfloor\right)$. $m$ divides $n$. on function symbols: derivatives with respect to argument.

The main function treated in this chapter is the Riemann zeta function $\zeta\left(s\right)$. This notation was introduced in Riemann (1859).

The main related functions are the Hurwitz zeta function $\zeta\left(s,a\right)$, the dilogarithm $\mathrm{Li}_{2}\left(z\right)$, the polylogarithm $\mathrm{Li}_{s}\left(z\right)$ (also known as Jonquière’s function $\phi\left(z,s\right)$), Lerch’s transcendent $\Phi\left(z,s,a\right)$, and the Dirichlet $L$-functions $L\left(s,\chi\right)$.