A reflection relation is a functional equation relating 
to 
, or more generally, 
to 
.
Perhaps the best known example of a reflection formula is the gamma function identity
 | (1) |
originally discovered by Euler (Havil 2003, pp. 58-59).
The reflection relation for the Riemann zeta function 
is given by
 | (2) |
where
 | (3) |
and 
is the gamma function, as first suggested by Euler in 1761 (Havil 2003, p. 193).
The xi-function has the reflection relation
 | (4) |
(Havil 2003, p. 203).
The Barnes G-function satisfies
 | (5) |
The Rogers L-function satisfies
 | (6) |
The tau Dirichlet series 
satisfies the reflection relation
 | (7) |
(Hardy 1999, p. 173).
