Table of Singular Moduli
(Collected and checked by V.V.Petrović)
Contains values of 124 singular moduli
IntroductionThis site is dedicated to singular moduli, which are characteristic arguments (elliptic moduli) of the function
f(k)=K(k)/K'(k), for which f(k)=1/Sqrt(n), n=1,2,3,... . Here, K(k) is the complete elliptic integral of the first kind and K'(k)=K(Sqrt(1-k^2)).
Singular moduli are given here as symbolic expressions (thus they are exact) and not as numerical values, and are arranged in a table. Table is given in two forms, as a standard pdf text document and as a Mathematica notebook. The second form could be particularly useful if one wants to use values from the table and include them in some other document or a computer program.
The topic of singular moduli is connected to various mathematical topics and disciplines, and not only to special functions. The reader who is interested in more theory on this topic can consult a large number of books on special functions, few of which are listed as references at this site.
I would be grateful for any comment or suggestion concerning this site.
V.V.Petrović, Univ. of Belgrade, School EE (ETF)
External linksElliptic Integral Singular Value
(from Wolfram Research Mathworld)