Jacobi Theta Functions

Functions to compute the Jacobi theta functions \((\theta_1, \theta_2, \theta_3, \theta_4)\) parameterised by either \((q)\) or \((\tau)\).

Usage

jacobi_theta1(x, q)

jacobi_theta1tau(x, tau)

jacobi_theta2(x, q)

jacobi_theta2tau(x, tau)

jacobi_theta3(x, q)

jacobi_theta3tau(x, tau)

jacobi_theta3m1(x, q)

jacobi_theta3m1tau(x, tau)

jacobi_theta4(x, q)

jacobi_theta4tau(x, tau)

jacobi_theta4m1(x, q)

jacobi_theta4m1tau(x, tau)

Arguments

x

Input value

q

The nome parameter of the Jacobi theta function (0 < q < 1)

tau

The nome parameter of the Jacobi theta function (tau = u + iv, where u and v are real numbers)

Value

A single numeric value with the computed Jacobi theta function.

See also

Boost Documentation for more details on the mathematical background.

Examples

# Jacobi Theta Functions
x <- 0.5
q <- 0.9
tau <- 1.5
jacobi_theta1(x, q)
#> [1] 0.0001025529
jacobi_theta1tau(x, tau)
#> [1] 0.2951461
jacobi_theta2(x, q)
#> [1] 0.5090257
jacobi_theta2tau(x, tau)
#> [1] 0.5403556
jacobi_theta3(x, q)
#> [1] 0.5090257
jacobi_theta3tau(x, tau)
#> [1] 1.009707
jacobi_theta3m1(x, q)
#> [1] -0.4909743
jacobi_theta3m1tau(x, tau)
#> [1] 0.00970738
jacobi_theta4(x, q)
#> [1] 0.0001025529
jacobi_theta4tau(x, tau)
#> [1] 0.9902926
jacobi_theta4m1(x, q)
#> [1] -0.9998974
jacobi_theta4m1tau(x, tau)
#> [1] -0.009707391