In mathematics, the Chowla–Selberg formula is the evaluation of a certain product of values of the gamma function at rational values in terms of values of the Dedekind eta function at imaginary quadratic irrational numbers.
The result was essentially found by Lerch (1897) and rediscovered by Chowla and Selberg (1949, 1967).
The sum is taken over 0 < r < D, with the usual convention χ(r) = 0 if r and D have a common factor.
By combining this with the theory of complex multiplication, one can give a formula for the individual absolute values of the eta function as for some algebraic number α.
Using Euler's reflection formula for the gamma function gives: