Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions > Elliptic Functions >
Built-in Mathematica SymbolTutorials »|See Also »|More About »

EllipticTheta

EllipticTheta[a, u, q]
gives the theta function theta_a(u,q) (a=1,...,4).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • theta_1(u,q)=2q^(1/4)sum_(n=0)^(infty)(-1)^nq^(n(n+1))sin((2 n+1)u).
  • theta_2(u,q)=2q^(1/4)sum_(n=0)^(infty)q^(n(n+1))cos((2 n+1)u).
  • theta_3(u,q)=1+2sum_(n=1)^(infty)q^(n^2)cos(2n u).
  • theta_4(u,q)=1+2sum_(n=1)^(infty)(-1)^nq^(n^2)cos(2n u).
  • The theta_i are defined only inside the unit q disk; the disk forms a natural boundary of analyticity.
  • Inside the unit q disk, theta_1 and theta_2 have branch cuts from 0 to -1.
  • For certain special arguments, EllipticTheta automatically evaluates to exact values.
New in 1
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team