§25.1 Special Notation ‣ Notation ‣ Chapter 25 Zeta and Related Functions (original) (raw)
| k,m,n | nonnegative integers. |
|---|---|
| p | prime number. |
| x | real variable. |
| a | real or complex parameter. |
| s=σ+it | complex variable. |
| z=x+iy | complex variable. |
| γ | Euler’s constant (§5.2(ii)). |
| ψ(x) | digamma functionΓ′(x)/Γ(x)except in §25.16. See §5.2(i). |
| Bn,Bn(x) | Bernoulli number and polynomial (§24.2(i)). |
| B~n(x) | periodic Bernoulli functionBn(x−⌊x⌋). |
| m|n | m divides n. |
| primes | on function symbols: derivatives with respect to argument. |
The main function treated in this chapter is the Riemann zeta functionζ(s). This notation was introduced in Riemann (1859).
The main related functions are the Hurwitz zeta function ζ(s,a), the dilogarithm Li2(z), the polylogarithm Lis(z)(also known as Jonquière’s function ϕ(z,s)), Lerch’s transcendent Φ(z,s,a), and the Dirichlet L-functionsL(s,χ).