JacobiTheta1
The Jacobi theta function theta1
JacobiTheta2
The Jacobi theta function theta2
JacobiTheta3
The Jacobi theta function theta3
JacobiTheta4
The Jacobi theta function theta4
Calling Sequence
Parameters
Description
Examples
JacobiTheta1(z, q)
JacobiTheta2(z, q)
JacobiTheta3(z, q)
JacobiTheta4(z, q)
z
-
algebraic expression (the parameter)
q
algebraic expression (the nome) such that q<1
The Jacobi theta functions JacobiTheta1, JacobiTheta2, JacobiTheta3, JacobiTheta4 are defined by:
JacobiTheta1z,q=2q1/4∑n=0∞−1nqnn+1sin2n+1z
JacobiTheta2z,q=2q1/4∑n=0∞qnn+1cos2n+1z
JacobiTheta3z,q=1+2∑n=1∞qn2cos2nz
JacobiTheta4z,q=1+2∑n=1∞−1nqn2cos2nz
These series converge very fast for q<1. See Chapter 16, "Jacobian Elliptic Functions and Theta Functions" of Handbook of Mathematical Functions edited by Abramowitz and Stegun for more extensive information.
JacobiTheta12.0,0.5
1.632025903
JacobiTheta22.0,0.5
−0.3181628217
JacobiTheta32.0,0.5
0.3314359783
JacobiTheta42.0,0.5
1.632130562
See Also
EllipticNome
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