# §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 $\mathop{\Gamma\/}\nolimits'\!\left(x\right)/\mathop{\Gamma\/}\nolimits\!\left(% x\right)$ except in §25.16. See §5.2(i). Bernoulli number and polynomial (§24.2(i)). periodic Bernoulli function $\mathop{B_{n}\/}\nolimits\!\left(x-\left\lfloor x\right\rfloor\right)$. $m$ divides $n$. on function symbols: derivatives with respect to argument.

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

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