§25.1 Special Notation

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Keywords:: Jonquière’s function, Riemann zeta function, notation, zeta function
Permalink:: http://dlmf.nist.gov/25.1
See also:: Annotations for Ch.25

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

$k, m, n$	nonnegative integers.
$p$	prime number.
$x$	real variable.
$a$	real or complex parameter.
$s=\sigma+it$	complex variable.
$z=x+iy$	complex variable.
$\gamma$	Euler’s constant (§5.2(ii)).
$\psi\left(x\right)$	digamma function $\Gamma'\left(x\right)/\Gamma\left(x\right)$ except in §25.16. See §5.2(i).
$B_{n},B_{n}\left(x\right)$	Bernoulli number and polynomial (§24.2(i)).
$\widetilde{B}_{n}\left(x\right)$	periodic Bernoulli function $B_{n}\left(x-\left\lfloor x\right\rfloor\right)$ .
$m\mathbin{\|}n$	$m$ divides $n$ .
primes	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 $\operatorname{Li}_{2}\left(z\right)$ , the polylogarithm $\operatorname{Li}_{s}\left(z\right)$ (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 $L\left(s,\chi\right)$ .

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