boostmath (version 1.0.0)

jacobi_theta_functions: Jacobi Theta Functions

Description

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)

Value

A single numeric value with the computed Jacobi theta function.

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)

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)
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)